Search any question & find its solution
Question:
Answered & Verified by Expert
$A$ and $B$ are two independent events. The probability that both $A$ and $B$ occur is $\frac{1}{6}$ and the probability that neither of them occurs is $\frac{1}{3}$. Then the probability of the two events are respectively
Options:
Solution:
1029 Upvotes
Verified Answer
The correct answer is:
$\frac{1}{2}$ and $\frac{1}{3}$
$P(A \cap B)=P(A) \cdot P(B)=\frac{1}{6}$
$P(\bar{A} \cap \bar{B})=\frac{1}{3}=1-P(A \cup B)$
$\Rightarrow \frac{1}{3}=1-[P(A)+P(B)]+\frac{1}{6} \Rightarrow P(A)+P(B)=\frac{5}{6}$.
Hence $P(A)$ and $P(B)$ are $\frac{1}{2}$ and $\frac{1}{3}$.
$P(\bar{A} \cap \bar{B})=\frac{1}{3}=1-P(A \cup B)$
$\Rightarrow \frac{1}{3}=1-[P(A)+P(B)]+\frac{1}{6} \Rightarrow P(A)+P(B)=\frac{5}{6}$.
Hence $P(A)$ and $P(B)$ are $\frac{1}{2}$ and $\frac{1}{3}$.
Looking for more such questions to practice?
Download the MARKS App - The ultimate prep app for IIT JEE & NEET with chapter-wise PYQs, revision notes, formula sheets, custom tests & much more.