If A and B are two events such that  find P(not A and not B).

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 Multiple Choice QuestionsShort 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).


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 comma space space straight P left parenthesis straight A intersection straight B right parenthesis space equals space 1 over 8
Now,      straight P left parenthesis straight A space intersection space straight B right parenthesis space equals space 1 over 8 space equals 1 fourth cross times 1 half space equals space straight P left parenthesis straight A right parenthesis cross times straight P left parenthesis straight B right parenthesis comma
therefore     A and B are independent
rightwards double arrow space space space space space space space straight A to the power of straight c space and space straight B to the power of straight c space are space also space independent.
rightwards double arrow space space space space space space straight P left parenthesis straight A to the power of straight c space intersection space straight B to the power of straight c right parenthesis space equals space straight P left parenthesis straight A to the power of straight c right parenthesis thin space straight P left parenthesis straight B to the power of straight c right parenthesis
rightwards double arrow space space space straight P left parenthesis not space straight A space and space not thin space straight B right parenthesis space equals space open square brackets 1 minus straight P left parenthesis straight A right parenthesis close square brackets space open square brackets 1 minus straight P left parenthesis straight B right parenthesis close square brackets
space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space equals space open parentheses 1 minus 1 fourth close parentheses space open parentheses 1 minus 1 half close parentheses space equals 3 over 4 cross times 1 half space equals 3 over 8.
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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).
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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.

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(B | A)

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