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Short Answer Type

801.

If P(A) = $3 over 5$ and $straight P left parenthesis straight B right parenthesis space equals space 1 third comma$ find:
(i) P(A or B), if A and B are mutually exclusive events.
(ii) P (A and B), if A and B are independent events.

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802. If A and B are two events such that

straight P left parenthesis straight A right parenthesis space equals space 1 fourth comma space space straight P left parenthesis straight B right parenthesis space equals space 1 half space and space straight P left parenthesis straight A intersection straight B right parenthesis space equals space 1 over 8 comma

find P(not A and not B).

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803. Given two independent events A and B such that P(A) = 0.3, P(B) = 0.6. Find P(A and B).

Here P(A) = 0.3, P(B) = 0.6
$therefore space space space space space space space space space space straight P space open parentheses straight A with bar on top close parentheses equals space 1 minus straight P left parenthesis straight A right parenthesis space equals space 1 minus 0.3 space equals 0.7 space space space space space space space space space space space space space straight P open parentheses straight B with bar on top close parentheses space equals space 1 minus space straight P left parenthesis straight B right parenthesis space equals space 1 minus 0.6 space equals space 0.4$
P(A and B) = P(A) x P(B) [ $because$ A and B are independent]
= 0.3 x 0.6 = 0.18

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804. Given two independent events A and B such that P(A) = 0.3, P(B) = 0.6. Find P(A and not B).

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805. Given two independent events A and B such that P(A) = 0.3, P(B) = 0.6. Find P(A or B).

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806. Given two independent events A and B such that P(A) = 0.3, P(B) = 0.6. Find P(neither A nor B)

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807. A die is thrown. If E is the event ‘the number appearing is a multiple of 3’ and F be the event ‘the number appearing is even’ then find whether E and F are independent?

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808. An unbiased die is thrown twice. Let the event A be ‘odd number on the first throw’ and B the event ‘odd number on the second throw’. Check the independence of the events A and B.

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809.

If $straight P left parenthesis straight A right parenthesis space equals space 6 over 11 comma space space straight P left parenthesis straight B right parenthesis space equals space 5 over 11 space and space straight P left parenthesis straight A union straight B right parenthesis space equals space 7 over 11 comma$ find P(A | B) .

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810.

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