Question

If A and B are two events associated with a random experiment for which $P\left(A\right)=0.35,P\text{(A or B)}=0.85,\text{and P(A and B)}=\mathrm{0.15.}$Find P(only B).

• A. 0.85
• B. 0.5
• C. 0.36
• D. 0.75

Answer 1

The correct option is B 0.5

Given: P(A) = 0.35,
P(A or B) = 0.85,
P(A and B) = 0.15.

$P\left(AUB\right)=P\left(A\right)+P\left(B\right)-P(A\cap B)0.85=0.35+P\left(B\right)-0.150.85=0.20+P\left(B\right)0.85-0.20=P\left(B\right)P\left(B\right)=0.65\text{P(only B)}=P(A^{\prime }\cap B)\text{P(only B)}=P\left(B\right)-P(A\cap B)\text{P(only B)}=0.65-0.15\text{P(only B)}=0.50$