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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).

Here, P(A) = 0.8, P(B) = 0.5, P(B | A) = 0.4
Now, $straight P left parenthesis straight B space left enclose straight A right parenthesis end enclose space equals space fraction numerator straight P left parenthesis straight B space intersection space straight A right parenthesis over denominator straight P left parenthesis straight A right parenthesis end fraction$
$rightwards double arrow space space space space space space 0.4 space equals space fraction numerator straight P left parenthesis straight A intersection straight B right parenthesis over denominator 0.8 end fraction space space rightwards double arrow space space space space straight P left parenthesis straight A intersection straight B right parenthesis space equals space 0.32$

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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?

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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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