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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).

91 Views

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

84 Views

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).

123 Views

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)

Since fair die is rolled
$therefore space space space straight S space equals space open curly brackets 1 comma space 2 comma space 3 comma space 4 comma space 5 comma space 6 close curly brackets.$
   $straight E space equals open curly brackets 1 comma space 3 comma space 5 close curly brackets comma space space space straight F space equals space open curly brackets 2 comma space 3 comma close curly brackets comma space space straight G space equals space open curly brackets 2 comma space 3 comma space 4 comma space 5 close curly brackets$
   $straight E union straight F space equals space open curly brackets 1 comma space 2 comma space 3 comma space 5 close curly brackets comma space space straight E intersection straight F space equals open curly brackets 3 close curly brackets left parenthesis straight E union straight F right parenthesis space intersection space straight G space equals space open curly brackets 2 comma space 3 comma space 5 close curly brackets comma space space left parenthesis straight E intersection straight F right parenthesis space intersection straight G space equals space open curly brackets 3 close curly brackets straight P open parentheses left parenthesis straight E union straight F right parenthesis space intersection straight G close parentheses space equals space 3 over 6 comma space space space straight P open parentheses left parenthesis straight E space intersection straight F right parenthesis space intersection space straight G close parentheses space equals 1 over 6$
$therefore space space straight P open parentheses left parenthesis straight E space union straight F right parenthesis space left enclose straight G close parentheses space equals space fraction numerator straight P left parenthesis left parenthesis straight E union straight F right parenthesis space intersection straight G right parenthesis over denominator straight P left parenthesis straight G right parenthesis end fraction space equals space fraction numerator begin display style 3 over 6 end style over denominator begin display style 4 over 6 end style end fraction space equals 3 over 4$

and $straight P left parenthesis left parenthesis straight E union straight F space left enclose straight G right parenthesis end enclose space equals space fraction numerator straight P left parenthesis left parenthesis straight E union straight F right parenthesis thin space intersection straight G right parenthesis over denominator straight P left parenthesis straight G right parenthesis end fraction space equals fraction numerator begin display style 3 over 6 end style over denominator begin display style 4 over 6 end style end fraction space equals space 3 over 4$
and $straight P left parenthesis left parenthesis straight E space intersection space straight F right parenthesis space left enclose straight G right parenthesis space equals space fraction numerator straight P left parenthesis left parenthesis straight E intersection straight F right parenthesis thin space intersection straight G right parenthesis over denominator straight P left parenthesis straight G right parenthesis end fraction space equals space fraction numerator begin display style 1 over 6 end style over denominator begin display style 4 over 6 end style end fraction space equals 1 fourth$

78 Views

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.

506 Views

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?

185 Views

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?

311 Views

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

Previous Year Papers

Test Series

Test Yourself

Short Answer Type

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)

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)