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) P(A and bar B)

Answer 1

(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 \(\overline{B}\) ) 

Formula used : P(A and \(\overline{B}\) ) = P(A) – P(A and B) 

Substituting in the above formula we get,

P(A and \(\overline{B}\) ) = 0.25 – 0.15 

P(A and \(\overline{B}\) ) = 0.10 

P(A and \(\overline{B}\)) = 0.10