Question

If A and B be two events associated with a random experiment such that P(A) = 0.3, P(B) = 0.2 and P(A ∩ B) = 0.1, find

(i) P(\(\overline{A}\)∩B)

(ii) P(A∩\(\overline{B}\))

Answer 1

(i) Given : P(A) = 0.3, P(B) = 0.2 , P(A ∩ B) = 0.1

To find :  P(\(\overline{A}\)∩B)

Formula used :  P(\(\overline{A}\)∩B) = P(B) - P(A ∩ B)

Substituting in the above formula we get

 P(\(\overline{A}\)∩B) = 0.2 – 0.1

 P(\(\overline{A}\)∩B) = 0.1

 P(\(\overline{A}\)∩B) = 0.1

(ii) Given : P(A) = 0.3, P(B) = 0.2 , P(A ∩ B) = 0.1

To find :   P(A∩\(\overline{B}\))

Formula used :   P(A∩\(\overline{B}\))  = P(A) - P(A ∩ B) 

Substituting in the above formula we get,

  P(A∩\(\overline{B}\)) = 0.3 – 0.1

  P(A∩\(\overline{B}\)) = 0.2

  P(A∩\(\overline{B}\)) = 0.2