Chances and Probability in Real World Problems: Worksheets, Online Test and Calculators

Chances and probability in real world problems worksheets, solved worksheet problems or exercises with step-by-step work, formative assessment as online test, calculator and more learning resources to learn, practice, assess and master the basic math skills of statistics.

Chances and Probability in Real World Problems

Name Grade School
Date Questions14 Score

1
When a dice is rolled, find the probability to get the number which is greater than 3?
2
What is the probability of getting a king from a deck of cards?
3
A coin is tossed 1000 times with the following frequencies (i)Head:780 (ii)Tail:220. compute the probability for each event.
4
Two unbiased coins are tossed simultaneously find the probability of getting (i)two heads (ii)one head (iii)at least one head (iv)at most one head.
5
Two dice are thrown simultaneously. Find the probability of getting (i)sum is equal to 4 (ii)an even number as the sum.
6
A bag contains 10 red and 8 blue balls. One ball is drawn at random. Find the probability that the ball drawn is blue.
7
1500 families were surveyed and following data was recorded about their maids at homes. A family is selected at random. Find the probability that the family selected has (i)Both types of maids (ii)Part time maids (iii)No maids
Types of maidsOnly part timeOnly full timeBoth
Number of families860370250
8
1500 families with 2 children were selected randomly, and the following data were recorded.Compute the probability of a family, chosen at random, having (i)2 girls (ii)1 girl (iii)No girl.
Number of girls in a family210
number of families475814211
9
If a probability of a player winning a particular tennis match is 0.72. What is the probability of the player loosing the match?
10
A company manufactures 1000 Computers in 6 months. Out of which 38 of them are found to be defective. When you choose one Computer from the manufactured, what is the probability that selected Computer is a good one.
11
The record of a weather station shows that out of the past 300 consecutive days, its weather was forecasted correctly 195 times. What is the probability that on a given day selected at random, (i)it was correct (ii)it was not correct.
12
There are 24 balls in a pot. If 3 of them are Red, 5 of them are Blue and the remaining are Green then, what is the probability of picking out (i)a Blue ball, (ii)a Red ball and (iii)a Green ball?
13
In a football match, a goalkeeper of a team can stop the goal, 32 times out of 40 attempts tried by a team. Find the probability that the opponent team can convert the attempt into a goal.
14
Eleven bags of wheat flour, each marked 5 kg, actually contained the following weights of flour (in kg). 4.97, 5.05, 5.08, 5.03, 5.00, 5.06, 5.08, 4.98, 5.04, 5.07, 5.00. Find the probability that any of these bags chosen at random contains more than 5 kg of flour.

Answers Key
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1
When a dice is rolled, find the probability to get the number which is greater than 3?
Probability to get the number which is greater than 3 is 1/2
Solution
Sample space for a dice, S= {1, 2, 3, 4, 5, 6}

Let E be the event of getting a number greater than 3
 E = {4,5,6}

P(E) = n(E)/n(S)

where n(E) = Number of Successful Events,
n(S) = Total Events of Sample Space

P(E) = 3/6

∴ Probability to get the number which is greater than 3= 1/2
2
What is the probability of getting a king from a deck of cards?
∴ Probability of getting a king from a deck of cards is 1/13
Solution
Sample space for a deck of cards, S = {spade (Ace, 2, 3, 4, 5, 6, 7, 8, 9,10, Jack, Queen, King), clubs (Ace, 2, 3, 4, 5, 6, 7, 8, 9,10, Jack, Queen, King), heart (Ace, 2, 3, 4, 5, 6, 7, 8, 9,10, Jack, Queen, King), diamond (Ace, 2, 3, 4, 5, 6, 7, 8, 9,10, Jack, Queen, King)}

Let E be the event of getting a king from a deck of cards
 E = {spade king, clubs king, heart king, diamond king}

P(E) = n(E)/n(S)

where n(E) = Number of Successful Events,
n(S) = Total Events of Sample Space

P(E) = 4/52

∴ Probability of getting a king from a deck of cards= 1/13
3
A coin is tossed 1000 times with the following frequencies (i)Head:780 (ii)Tail:220. compute the probability for each event.
(i) Probability of getting a head is 39/50
(ii) Probability of getting a tail is 11/50
Solution
Total number of trials, n(S) = 1000
Number of heads, n(H) = 780
Number of tails, n(T) = 220

(i) P(H) = n(H)/n(S)

where n(H) = Number of heads,
n(S) = Total number of trials

  P(H) = 780/1000
  ∴ Probability of getting a head, P(H)= 39/50

(ii) P(T) = n(T)/n(S)

where n(T) = Number of tails,
n(S) = Total number of trials

  P(T) = 220/1000
  ∴ Probability of getting a tail, P(T)= 11/50

Result
(i) Probability of getting a head is 39/50
(ii) Probability of getting a tail is 11/50
4
Two unbiased coins are tossed simultaneously find the probability of getting (i)two heads (ii)one head (iii)at least one head (iv)at most one head.
(i) Probability of getting two heads is 1/4
(ii) Probability of getting one head is 1/2
(iii) Probability of getting at least one head is 3/4
(iv) Probability of getting at most one head is 3/4
Solution
Sample space when two coins are tossed (S) = {HH, TT, HT, TH}

Event of getting two heads, (A)= {HH}
Event of getting one head, (B)= {HT,TH}
Event of getting at least one head, (C)= {HH,TH,HT}
Event of getting at most one head, (D)= {HH,HT,TH}

(i) Probability of getting two heads, P(A)= n(A)/n(S)
  P(A) = 1/4

(ii) Probability of getting one head, P(B)= n(B)/n(S)
  P(B) = 2/4

(iii) Probability of getting at least one head, P(C)= n(C)/n(S)
  P(C) = 3/4

(iv) Probability of getting at most one head, P(D)= n(D)/n(S)
  P(D) = 3/4

Result
(i) Probability of getting two heads is 1/4
(ii) Probability of getting one head is 1/2
(iii) Probability of getting at least one head is 3/4
(iv) Probability of getting at most one head is 3/4
5
Two dice are thrown simultaneously. Find the probability of getting (i)sum is equal to 4 (ii)an even number as the sum.
(i)Probability of getting sum is equal to 4 is 1/12
(ii) Probability of getting even number as the sum is 1/2
Solution
Sample space for two dice, S = 36
Possible outcomes of two dice are given below,
  (1,1), (1,2), (1,3), (1,4), (1,5), (1,6)
  (2,1), (2,2), (2,3), (2,4), (2,5), (2,6)
  (3,1), (3,2), (3,3), (3,4), (3,5), (3,6)
  (4,1), (4,2), (4,3), (4,4), (4,5), (4,6)
  (5,1), (5,2), (5,3), (5,4), (5,5), (5,6)
  (6,1), (6,2), (6,3), (6,4), (6,5), (6,6)

(i) Event of getting sum is equal to 4, (E) are given below,
  (1,3)  (2,2)  (3,1)     
  P(E) = n(E)/n(S)

where n(E) = Number of Successful Events,
n(S) = Number of Successful Events

  P(E) = 3/36
 ∴ Probability of getting sum is equal to 4, P(E)= 1/12

(ii) Event of getting even number as the sum, (E) are given below,
  (1,1), (1,3), (1,5)
  (2,2), (2,4), (2,6)
  (3,1), (3,3), (3,5)
  (4,2), (4,4), (4,6)
  (5,1), (5,3), (5,5)
  (6,2), (6,4), (6,6)
  P(E) = n(E)/n(S)

where n(E) = Number of Successful Events,
n(S) = Number of Successful Events

  P(E) = 18/36
 ∴ Probability of getting even number as the sum, P(E)= 1/2

Result
(i) Probability of getting sum is equal to 4 is 1/12
(ii) Probability of getting even number as the sum is 1/2
6
A bag contains 10 red and 8 blue balls. One ball is drawn at random. Find the probability that the ball drawn is blue.
Probability of getting blue ball is 4/9
Solution
Total number of balls, n(S)= 18
Event of getting red ball, n(R)= 10
Event of getting blue ball, n(B)= 8

Probability of getting blue ball, P(B)= n(B)/n(S)
P(B)= 8/18
Probability, P(B)= 4/9

∴ Probability of getting blue ball is 4/9
7
1500 families were surveyed and following data was recorded about their maids at homes. A family is selected at random. Find the probability that the family selected has (i)Both types of maids (ii)Part time maids (iii)No maids
Types of maidsOnly part timeOnly full timeBoth
Number of families860370250
(i)Probability that family selected has both types of maids is 1/6
(ii) Probability that family selected has part time maids is 43/75
(iii) Probability that family selected has no maids is 1/75
Solution
Total families, n(S)= 1500
Only part time maids, n(P)= 860
Only full time maids, n(F)= 370
Both, n(B) = 250

(i) Probability that family selected have both types of maids, P(B)= n(B)/n(S)
  P(B)= 250/1500
  Probability, P(B)= 1/6

(ii) Probability that family selected have part time maids, P(P)= n(P)/n(S)
  P(P)= 860/1500
  Probability, P(P)= 43/75

(iii) Family selected have maids= n(P)+n(F)+n(B)
 ∴ Family selected have maids= 860+370+250 = 1480
  Family selected have no maids, n(N)= 1500-1480 = 20
  Probability that family selected have no maids, P(N)= n(N)/n(S)
  P(N)= 20/1500
  Probability, P(N)= 1/75

Result
(i) Probability that family selected has both types of maids is 1/6
(ii) Probability that family selected has part time maids is 43/75
(iii) Probability that family selected has no maids is 1/75
8
1500 families with 2 children were selected randomly, and the following data were recorded.Compute the probability of a family, chosen at random, having (i)2 girls (ii)1 girl (iii)No girl.
Number of girls in a family210
number of families475814211
(i) Probability of a family having 2 girls is 19/60
(ii) Probability of a family having 1 girl is 407/750
(iii) Probability of a family having no girl is 211/1500
Solution
Total families, n(S) = 1500
Numbers of families having 2 girls, n(A)= 475
Numbers of families having 1 girl, n(B)= 814
Numbers of families having no girl, n(C)= 211

(i) Probability of a family having 2 girls, P(A)= n(A)/n(S)
  P(A) = 475/1500
  Probability, P(A)= 19/60

(ii) Probability of a family having 1 girl, P(B)= n(B)/n(S)
  P(B) = 814/1500
  Probability, P(B)= 407/750

(iii) Probability of a family having no girls, P(C)= n(C)/n(S)
  P(C) = 211/1500
  Probability, P(C)= 211/1500

Result
(i) Probability of a family having 2 girls is 19/60
(ii) Probability of a family having 1 girl is 407/750
(iii) Probability of a family having no girl is 211/1500
9
If a probability of a player winning a particular tennis match is 0.72. What is the probability of the player loosing the match?
Probability that it will not rain tomorrow is 0.28
Solution
Let E be the event that it will rain tomorrow
and E` be the event that it will not rain tomorrow
P(E) = 0.72
P(E`) = 1-0.72 = 0.28

∴ Probability that it will not rain tomorrow= 0.28
10
A company manufactures 1000 Computers in 6 months. Out of which 38 of them are found to be defective. When you choose one Computer from the manufactured, what is the probability that selected Computer is a good one.
Probability that selected Computer is a good one is 481/500
Solution
Total computers, n(S)= 1000
Defective computers, n(D)= 38
Number of good computers, n(G)= 1000-38 = 962

Probability that selected Computer is a good one, P(G)= n(G)/n(S)
P(G) = 962/1000
Probability, P(G)= 481/500

∴ Probability that selected Computer is a good one is 481/500
11
The record of a weather station shows that out of the past 300 consecutive days, its weather was forecasted correctly 195 times. What is the probability that on a given day selected at random, (i)it was correct (ii)it was not correct.
(i) The number of days when the forecast was correct is 13/20
(ii) The number of days when the forecast was not correct is 7/20
Solution
Total number of days, n(S)= 300

(i) The number of days when the forecast was correct, n(C)= 195
  Probability that selected day selected was correct, P(C)= n(C)/n(S)
  P(C)= 195/300
  Probability, P(C) = 13/20

(ii) The number of days when the forecast was not correct, n(N)= n(S)-n(C)
 ∴ n(N) = 300-195 =105
  Probability that selected day selected was not correct, P(N)= n(N)/n(S)
  P(N) = 105/300
  Probability, P(N)= 7/20

Result
(i) The number of days when the forecast was correct is 13/20
(ii) The number of days when the forecast was not correct is 7/20
12
There are 24 balls in a pot. If 3 of them are Red, 5 of them are Blue and the remaining are Green then, what is the probability of picking out (i)a Blue ball, (ii)a Red ball and (iii)a Green ball?
(i) Probability of picking out blue ball is 5/24
(ii) Probability of picking out red ball is 1/8
(iii) Probability of picking out green ball is 2/3
Solution
Total number of balls, n(S)= 24
Number of red balls, n(R)= 3
Number of blue balls, n(B)= 5

(i) Probability of picking out blue ball, P(B)= n(B)/n(S)
  P(B)= 5/24
  Probability, P(B)= 5/24

(ii) Probability of picking out red ball, P(R)= n(R)/n(S)
  P(R)= 3/24
  Probability, P(R)= 1/8

(iii) Number of green ball, n(G)= n(S)-n(R)+n(B)
  n(G)= 24-(3+5)
  n(G)= 16
  Probability of picking out green ball, P(G)= n(G)/n(S)
  P(G)= 16/24
  Probability, P(G)= 2/3

Result
(i) Probability of picking out blue ball is 5/24
(ii) Probability of picking out red ball is 1/8
(iii) Probability of picking out green ball is 2/3
13
In a football match, a goalkeeper of a team can stop the goal, 32 times out of 40 attempts tried by a team. Find the probability that the opponent team can convert the attempt into a goal.
Probability of attempts by opponent team is 1/5
Solution
Total number of attempts, n(S)= 40
Number of attempts by a team, n(A)= 32

Number of attempts by opponent team, n(B)= n(S)-n(A)
n(B)= 40-32
n(B)= 8
Probability of attempts by opponent team, P(B)= n(B)/n(S)
P(B)= 8/40
Probability, P(B)= 1/5

∴ Probability of attempts by opponent team is 1/5
14
Eleven bags of wheat flour, each marked 5 kg, actually contained the following weights of flour (in kg). 4.97, 5.05, 5.08, 5.03, 5.00, 5.06, 5.08, 4.98, 5.04, 5.07, 5.00. Find the probability that any of these bags chosen at random contains more than 5 kg of flour.
Probability that bag chosen at random contains more than 5 kg of flour is 7/11
Solution
Total number of bags present, n(S)= 11
Number of bags containing more than 5 kg of flour, n(A)= 7

Probability that any of these bags chosen at random contains more than 5 kg of flour, P(A)= n(A)/n(S)
P(A)= 7/11
Probability, P(A)= 7/11

∴ Probability that bag chosen at random contains more than 5 kg of flour is 7/11

Worksheet: Chances and Probability in Real World Problems

Chances and probability in real world problems worksheet is the largest collection of practice problems and solved exercises which can be served as homework, classwork or assignment problems for the students to learn, practice, assess, iterate and master the skills of how to solve such statistics problems in basic mathematics.

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Two dice are thrown simultaneously. Find the probability of getting (i) sum is equal to 5 (ii) an even number as the sum.
What is the probability of getting a Ace from a deck of cards?
There are 24 balls in a pot. If 10 of them are Red, 9 of them are Blue and the remaining are Green then, what is the probability of picking out a Green ball?
A coin is tossed 1000 times with the following frequencies (i) Head : 373 (ii) Tail : 627. compute the probability for each event.
A company manufactures 1000 Computers in 6 months. Out of which 45 of them are found to be defective. what is the probability that selected one is a good one.
When a dice is rolled, find the probability to get the number which is greater than 4?
Two unbiased coins are tossed simultaneously find the probability of getting (i) two tails (ii) one tail (iii) at least one tail (iv) at most one tail.
A bag contains 46 red and 38 blue balls. One ball is drawn at random. Find the probability that the ball drawn is blue.
The record of a weather station shows that out of the past 231 consecutive days, it was forecasted correctly 146 times. Find probability of selected day was correct.
If a probability of a player winning a particular tennis match is 0.09. What is the probability of the player loosing the match?

Online Test: Chances and Probability in Real World Problems

This online test to find the chances and probability in real world problems is a formative assessment which can be used as homework, classwork or assignment problems to assess and improve the learner's math skills on statistics.

Probability Calculator

Total Events n(S) :
Success Events n(A) :
Success Events n(B) :
Total Events n(S)52
Success Events n(A)4
Success Events n(B)3
P(A)0.08
P(A')0.92
P(B)0.06
P(B')0.94
P(A ∩ B)0.0048
P(A U B)0.1352
P(A | B)0.08
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Probability calculator is a key tool for users to generate step-by-step work to quickly understand the calculation, solve the homework problems, solve the classwork problems, prepare the answer key document for summative and formative assessments or immediately verify the entire calculation for the user supplied input values.