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Probability

Short Answer Type

741. If P( A) = 0.8, P(B) = 0.5 and P(B | A) = 0.4, find P(A ∩ B).

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742. If P( A) = 0.8, P(B) = 0.5 and P(B | A) = 0.4, find P(A | B).

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743. If P( A) = 0.8, P(B) = 0.5 and P(B | A) = 0.4, find P (A ∪ B)

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744.

A fair die is rolled. Consider events E = {1, 3, 5}, F = {2, 3} and G = {2, 3, 4, 5}. Find P(E|F) and P(F|E).

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745.

A fair die is rolled. Consider events E = {1, 3, 5}, F = {2, 3} and G = {2, 3, 4, 5}. Find P(E|G) and P(G|E).

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746.

A fair die is rolled. Consider events E = {1, 3, 5}, F = {2, 3} and G = {2, 3, 4, 5}. Find P((E ∪ F) | G) and P((E ∩ F) | G)

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747. 12 cards, numbered 1 to 12, are placed in a box, mixed up thoroughly and then a card is drawn at random from the box. If it is known that the number on the drawn card is more than 3, find the probability that it is an even number.

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748. Ten cards numbered 1 to 10 are placed in a box, mixed up thoroughly and then one card is drawn randomly. If it is known that the number on the drawn card is more than 3, what is the probability that it is an even number?

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749. In a school, there are 1000 students, out of which 430 are girls. It is known that out of 430, 10% of the girls study in class XII. What is the probability that a student chosen randomly studies in Class XII given that the chosen student is a girl?

Let E denote the event that a student chosen randomly studies in class XII and F be the event that the randomly chosen student is a girl.
Total number of students = 1000
Number of girls = 430
Number of girls studying in class XII =

10 over 100 cross times 430 space equals space 43

Now, P(F) =

430 over 1000 space equals space 0.43

and

straight P left parenthesis straight E intersection straight F right parenthesis space equals 43 over 1000 space equals 0.043

therefore space space space straight P left parenthesis straight E space left enclose straight F right parenthesis space equals space fraction numerator straight P left parenthesis straight E space intersection thin space straight F right parenthesis over denominator straight P left parenthesis straight F right parenthesis end fraction equals space fraction numerator 0.043 over denominator 0.43 end fraction space equals fraction numerator begin display style 43 over 1000 end style over denominator begin display style 43 over 100 end style end fraction equals space 43 over 100 cross times 100 over 43 space equals 1 over 10 space equals space 0.1

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750.

A die is thrown three times. Events A and B are defined as below:
A: 4 on the third throw
B: 6 on the first and 5 on the second throw
Find the probability of A given that B has already occurred.

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