For two events A and B, let P(A) = 0.4 and P(B) = p and P(A∪ B

Previous Year Papers

Download Solved Question Papers Free for Offline Practice and view Solutions Online.

Test Series

Take Zigya Full and Sectional Test Series. Time it out for real assessment and get your results instantly.

Test Yourself

Practice and master your preparation for a specific topic or chapter. Check you scores at the end of the test.
Advertisement

 Multiple Choice QuestionsShort Answer Type

791. If P(not A) = 0.4, P(A ∪ B) = 0.75 and A, B are given to be independent events, find the value of P(B).
73 Views

792. If P(not B) = 0.65, P( A ∪ B) = 0.85 and A, B are independent events, find the value of P(A).
92 Views

Advertisement

793.

For two events A and B, let P(A) = 0.4 and P(B) = p and P(A∪ B) = 0.6
(i) Find p so that A and B are independent events.
(ii) Find p so that A and B are mutually exclusive events.


straight P left parenthesis straight A right parenthesis space equals space 0.4 comma space space space straight P left parenthesis straight B right parenthesis space equals space straight p comma space space space straight P left parenthesis straight A union straight B right parenthesis space equals space 0.6
(i) Since A  and B are independent events
 therefore space space space space space space straight P left parenthesis straight A intersection straight B right parenthesis space equals space straight P left parenthesis straight A right parenthesis space straight P left parenthesis straight B right parenthesis                                       ...(1)
Now    straight P left parenthesis straight A union 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 minus space straight P left parenthesis straight A intersection straight B right parenthesis  
therefore space space space space space space space space space space space space space 0.6 space equals 0.4 space plus space straight p space minus space straight P left parenthesis straight A right parenthesis space straight P left parenthesis straight B right parenthesis space space space space space space space space space space space space open square brackets because space of space left parenthesis 1 right parenthesis close square brackets
therefore space space space space space space space space space space space space space 0.6 space equals space 0.4 space plus space straight p space minus space left parenthesis 0.4 right parenthesis space straight p space space rightwards double arrow space space 0.2 space equals space 0.6 space straight p
rightwards double arrow space space space space space space space space space space space space space straight p space equals space fraction numerator 0.2 over denominator 0.6 end fraction space equals 2 over 6 space equals 1 third
(ii) Since A and B are mutually exclusive events
therefore space space space space space space straight P left parenthesis straight A intersection straight B right parenthesis space equals space 0                                                     ...(2)
Now,   straight P left parenthesis straight A space union space straight B right parenthesis space equals space straight P left parenthesis straight A right parenthesis plus straight P left parenthesis straight B right parenthesis space minus space straight P left parenthesis straight A intersection straight B right parenthesis
therefore space space space space space space space space space space 0.6 space equals space 0.4 space plus space straight p space minus space 0 space space space rightwards double arrow space space space straight p space equals space 0.2 space equals space 1 fifth
72 Views

Advertisement
794. Given that the events A and B are such that P(A) =1 half comma   straight P left parenthesis straight A union straight B right parenthesis space equals space 3 over 5 space and space straight P left parenthesis straight B right parenthesis space equals space straight p. Find p if they are mutually exclusive.

90 Views

Advertisement
795. Given that the events A and B are such that P(A) =1 half comma   straight P left parenthesis straight A union straight B right parenthesis space equals space 3 over 5 space and space straight P left parenthesis straight B right parenthesis space equals space straight p. Find p if they are independent.

72 Views

796.

Let A and B be independent events with P(A) = 0.3 and P(B) = 0.4. Find P(A ∩ B)

95 Views

797.

Let A and B be independent events with P(A) = 0.3 and P(B) = 0.4. Find P(A ∪ B)

85 Views

798.

Let A and B be independent events with P(A) = 0.3 and P(B) = 0.4. Find P(A|B) 

86 Views

Advertisement
799.

Let A and B be independent events with P(A) = 0.3 and P(B) = 0.4. Find P(B | A)

96 Views

800. Events A and B are such that straight P left parenthesis straight A right parenthesis space equals space 1 half comma space straight P left parenthesis straight B right parenthesis space equals space 7 over 12 space and space straight P left parenthesis not space straight A space or space not space straight B right parenthesis space equals 1 fourth. State whether A and B are independent?
76 Views

Advertisement