If P(A) = 0.38, P(A ∪ B) = 0.69, find P(B), if A and B are independent events. - Wired Faculty

Question

If P(A) = 0.38, P(A ∪ B) = 0.69, find P(B), if A and B are independent events.

Solution

Here, P(A) = 0.38, $straight P left parenthesis straight A union straight B right parenthesis space equals space 0.69$
Let P(B) = p
Since A and B are independent.
$therefore$ $straight P left parenthesis straight A space intersection thin space straight B right parenthesis space equals straight P left parenthesis straight A right parenthesis space cross times space straight P left parenthesis straight B right parenthesis$
$therefore space space space space straight P left parenthesis straight A intersection straight B right parenthesis space equals space left parenthesis 0.38 right parenthesis thin space straight p$ ...(1)
Now $straight P left parenthesis straight A space union space straight B right parenthesis space equals space straight P left parenthesis straight A right parenthesis space plus space straight P left parenthesis straight B right parenthesis space minus space straight P left parenthesis straight A intersection straight B right parenthesis.$
$therefore space space space 0.69 space equals space 0.38 space plus space straight p space minus space left parenthesis 0.38 right parenthesis thin space straight p therefore space space space 0.31 space equals space 0.62 space straight p space space space space space space space space space space space space space space space space space space space space space space rightwards double arrow space space space space straight p space equals space fraction numerator 0.31 over denominator 0.62 end fraction therefore space space space space space straight p space equals space 31 over 62 space equals space 1 half therefore space space space straight P left parenthesis straight B right parenthesis space equals 1 half space equals space 0.5$

For Daily Free Study Material Join wiredfaculty

Probability

If P(A) = 0.38, P(A ∪ B) = 0.69, find P(B), if A and B are independent events.

Some More Questions From Probability Chapter

Mock Test Series

NCERT Sample Papers

Entrance Exams Preparation

Phone Number

Email Address

Loaction