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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?

Let A be the event ‘the number on the card drawn is even’ and B be the event ‘the number on the card drawn is greater than 3’.

therefore space space space space straight S space equals space open curly brackets 1 comma space 2 comma space 3 comma space 4 comma space 5 comma space 6 comma space 7 comma space 8 comma space 9 comma space 10 close curly brackets therefore space space straight A space equals space open curly brackets 2 comma space 4 comma space 6 comma space 8 comma space 10 close curly brackets comma space space space straight B space equals space open curly brackets 4 comma space 5 comma space 6 comma space 7 comma space 8 comma space 9 comma space 10 close curly brackets and space space space space space space straight A space intersection thin space straight B space equals open curly brackets 4 comma space 6 comma space 8 comma space 10 close curly brackets therefore space space space space space space space straight P left parenthesis straight A right parenthesis space equals space 5 over 10 comma space space space straight P left parenthesis straight B right parenthesis space equals space 7 over 10 space and space straight P left parenthesis straight A intersection straight B right parenthesis space equals space 4 over 10 therefore space space space space space space straight P left parenthesis straight A space left enclose space straight B right parenthesis end enclose space equals space fraction numerator straight P left parenthesis straight A intersection straight B right parenthesis over denominator straight P left parenthesis straight B right parenthesis end fraction space equals fraction numerator begin display style 4 over 10 end style over denominator begin display style 7 over 10 end style end fraction equals space 4 over 7.

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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.

422 Views