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)
(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
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
P(A and ) = 0.10