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Probability

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.

Here $straight P left parenthesis straight A right parenthesis space equals space 3 over 5 comma space space straight P left parenthesis straight B right parenthesis space equals 1 third$

(i) $straight P left parenthesis straight A space or space straight B right parenthesis space equals space straight P left parenthesis straight A right parenthesis space plus space straight P left parenthesis straight B right parenthesis space space space left square bracket because space straight A space and space straight B space are space mutually space exclusive space events right square bracket$

$equals space 3 over 5 plus 1 third space equals fraction numerator 9 plus 5 over denominator 15 end fraction space equals 14 over 15$

(ii) Since A and B are independent events
$straight P left parenthesis straight A space and space straight B right parenthesis space equals space straight P left parenthesis straight A right parenthesis space cross times space straight P left parenthesis straight B right parenthesis space equals space 3 over 5 cross times 1 third space space equals 1 fifth$

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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).

76 Views

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

90 Views

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.

163 Views

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) .