A fair die is rolled. Consider events E = {1, 3, 5}, F = {2, 3}

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 Multiple Choice QuestionsShort 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).


Since fair die is rolled
therefore 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 close curly brackets.
        straight E space equals open curly brackets 1 comma space 3 comma space 5 close curly brackets comma space space space straight F space equals space open curly brackets 2 comma space 3 comma close curly brackets comma space space straight G space equals space open curly brackets 2 comma space 3 comma space 4 comma space 5 close curly brackets

straight E intersection straight G space equals space open curly brackets 3 comma space 5 close curly brackets
therefore space space space straight P left parenthesis straight E right parenthesis space equals space 3 over 6 comma space space straight P left parenthesis straight G right parenthesis space equals space 4 over 6 comma space space straight P left parenthesis straight E space intersection space straight G right parenthesis space equals 2 over 6
therefore space space space space space straight P left parenthesis straight E space left enclose straight G right parenthesis end enclose space equals space fraction numerator straight P left parenthesis straight E intersection straight G right parenthesis over denominator straight P left parenthesis straight G right parenthesis end fraction space equals space fraction numerator begin display style 2 over 6 end style over denominator begin display style 4 over 6 end style end fraction equals space 2 over 4 space equals space 1 half
space space space space space space space space space space space space space space space straight P left parenthesis straight G space left enclose space straight E right parenthesis end enclose space equals space fraction numerator straight P left parenthesis straight G intersection straight E right parenthesis over denominator straight P left parenthesis straight E right parenthesis end fraction space equals space fraction numerator straight P left parenthesis straight E intersection straight G right parenthesis over denominator straight P left parenthesis straight E right parenthesis end fraction space equals space fraction numerator begin display style 2 over 6 end style over denominator begin display style 3 over 6 end style end fraction space equals space 2 over 3
space space space space space
          

  

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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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