An unbiased die is thrown twice. Let the event A be ‘odd numbe

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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).
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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.


straight S space equals space open curly brackets table row cell left parenthesis 1 comma space 1 right parenthesis end cell cell left parenthesis 1 comma space 2 right parenthesis end cell cell left parenthesis 1 comma space 3 right parenthesis end cell cell left parenthesis 1 comma space 4 right parenthesis end cell cell left parenthesis 1 comma space 5 right parenthesis end cell cell left parenthesis 1 comma space 6 right parenthesis end cell row cell left parenthesis 2 comma 1 right parenthesis end cell cell left parenthesis 2 comma space 2 right parenthesis end cell cell left parenthesis 2 comma space 3 right parenthesis end cell cell left parenthesis 2 comma space 4 right parenthesis end cell cell left parenthesis 2 comma space 5 right parenthesis end cell cell left parenthesis 2 comma space 6 right parenthesis end cell row cell left parenthesis 3 comma space 1 right parenthesis end cell cell left parenthesis 3 comma space 2 right parenthesis end cell cell left parenthesis 3 comma space 3 right parenthesis end cell cell left parenthesis 3 comma space 4 right parenthesis end cell cell left parenthesis 3 comma space 5 right parenthesis end cell cell left parenthesis 3 comma space 6 right parenthesis end cell row cell left parenthesis 4 comma space 1 right parenthesis end cell cell left parenthesis 4 comma space 2 right parenthesis end cell cell left parenthesis 4 comma space 3 right parenthesis end cell cell left parenthesis 4 comma space 4 right parenthesis end cell cell left parenthesis 4 comma space 5 right parenthesis end cell cell left parenthesis 4 comma space 6 right parenthesis end cell row cell left parenthesis 5 comma space 1 right parenthesis end cell cell left parenthesis 5 comma space 2 right parenthesis end cell cell left parenthesis 5 comma space 3 right parenthesis end cell cell left parenthesis 5 comma space 4 right parenthesis end cell cell left parenthesis 5 comma space 5 right parenthesis end cell cell left parenthesis 5 comma space 6 right parenthesis end cell row cell left parenthesis 6 comma space 1 right parenthesis end cell cell left parenthesis 6 comma space 2 right parenthesis end cell cell left parenthesis 6 comma space 3 right parenthesis end cell cell left parenthesis 6 comma space 4 right parenthesis end cell cell left parenthesis 6 comma space 5 right parenthesis end cell cell left parenthesis 6 comma space 6 right parenthesis end cell end table close curly brackets
Number of elements (outcomes) of the above example space is 6 x 6  = 36.

                                 straight P left parenthesis straight A right parenthesis space equals 18 over 36 space equals 1 half space space and space straight P left parenthesis straight B right parenthesis space equals space 18 over 36 space equals 1 half

   Also comma space straight P left parenthesis straight A intersection straight B right parenthesis space equals space straight P thin space left parenthesis odd space number space on space both space throws right parenthesis
space space space space space space space space space space space space space space space space space equals space 9 over 36 space equals space 1 fourth

Now,   straight P left parenthesis straight A right parenthesis. space straight P left parenthesis straight B right parenthesis space equals space 1 half cross times 1 half space equals space 1 fourth

Clearly,   straight P left parenthesis straight A space intersection 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
∴ A and B are independent events.




                
  
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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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