If A and B are two events associated with a random experiment such that P(A) = 0.25, P(B) = 0.4 and P(A or B) = 0.5, find the values of

Question

If A and B are two events associated with a random experiment such that P(A) = 0.25, P(B) = 0.4 and P(A or B) = 0.5, find the values of (i) P(A and B) (ii)

Philoid · Accepted Answer

_(i)

Given : P(A) = 0.25, P(A or B) = 0.5 and P(B) = 0.4

To find : P(A and B)

Formula used : P(A or B) = P(A) + P(B) - P(A and B)

Substituting in the above formula we get,

0.5 = 0.25 + 0.4 – P(A and B)

0.5 = 0.65 - P(A and B)

P(A and B) = 0.65 – 0.5

P(A and B) = 0.15

(ii) Given : P(A) = 0.25, P(A and B) = 0.15 ( from part (i))

To find : P(A and )

Formula used : P(A and ) = P(A) – P(A and B)

Substituting in the above formula we get,

P(A and ) = 0.25 – 0.15

P(A and ) = 0.10

If A and B are two events associated with a random experiment such that P(A) = 0.25, P(B) = 0.4 and P(A or B) = 0.5, find the values of(i) P(A and B)(ii)

If A and B are two events associated with a random experiment such that P(A) = 0.25, P(B) = 0.4 and P(A or B) = 0.5, find the values of
(i) P(A and B)

(ii)