यदि P(A ∪ B) = 7/31, P(A ∩ B) = 24/31 तथा P(A) = 12/31 हो तो P(B) =

Question

यदि P(A ∪ B) = \(\frac 7{31}\), P(A ∩ B) = \(\frac {24}{31}\) तथा P(A) = \(\frac{12}{31}\) हो तो P(B) =

(A) \(\frac {15}{31}\)

(B) \(\frac {17}{31}\)

(C) \(\frac {19}{31}\)

(D) \(\frac {29}{31}\)

Answer 1

Correct option is (C) \(\frac {19}{31}\)

\(P(A \cup B) = P(A) + P(B) - P(A \cap B)\)

\(\frac 7{31} = \frac {12 }{31} + P(B) - \frac {24}{31}\)

\(P(B) = \frac 7{31} + \frac {24}{31} - \frac {12}{31}\)

\(= \frac{7 + 24 - 12}{31}\)

\(=\frac {19}{31}\)