CONDITIONAL PROBABILITY WORKSHEET

Problem 1 :

A pair of dice is thrown together and the sum of points of the two dice is noted to be 10. What is the probability that one of the two dice has shown the point 4?

Problem 2 :

In a group of 20 males and 15 females, 12 males and 8 females are service holders. What is the probability that a person selected at random from the group is a service holder given that the selected person is a male?

Answers

1. Answer :

Here, the condition is "The sum of points of the two dice is noted to be 10".

When a pair of dice is thrown together, n(S) = 36.

Let A be the event of getting sum of the points to be 10.

Then, A = {(4, 6), (5, 5), (6, 4)}.

n(A) = 3

P(A) = n(A)/n(S)

= 3/36

= 1/12

Let B be the event of getting 4 on one of the dice.

Then,

B = {(1, 4), (2, 4), (3, 4), (4, 1), (4, 2), (4, 3), (4, 5), (4, 6), (5, 4), (6, 4)}

AnB = {(4, 6), (6, 4)} ----> n(AnB) = 2

P(AnB) = n(AnB)/n(S)

= 2/36

= 1/18

Probability that one of the two dice has shown the point 4 with the condition "sum of points of the two dice to be 10" is

P(B/A) = P(AnB)/P(A)

= (1/18)/(1/12)

= (1/18) x (12/1)

= (1x12)/(18x1)

= 12/18

= 2/3

2. Answer :

Here, the condition is "The selected person is a male".

From, the given information, n(S) = 35.

Let A be the event of selecting a male person.

Then, n(A) = 20.

P(A) = n(A)/n(S)

= 20/35

= 4/7

Let B be the event of selecting a service holder.

Then, n(AnB) = 12.

P(AnB) = n(AnB)/n(S)

= 12/35

(Because, there are 12 male service holders)

The probability that a person selected at random from the group is a service holder given that the selected person is a male is

P(B/A)  =  P(AnB)/P(A)

= (12/35) / (20/35)

= (12/35) x (35/20)

= (12x35)/(35x20)

= 3/5

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