Two events X and Y are such that \(P(X)=\displaystyle\frac{1}{3}\), \(P(Y)=n\) and the probability of occurrence of at least one event is 0.8. If the events are independent, then the value of n is:
Answer & explanation
Correct answer: option 3
The correct answer is Option (3) → \(\displaystyle\frac{7}{10}\)
“At least one occurs” is the complement of “neither occurs”. Since X and Y are independent, so are X′ and Y′:
\(P(X\cup Y) = 1 - P(X')P(Y')\)
\( \displaystyle 0.8 = 1 - \frac{2}{3}(1 - n) \)
\( \displaystyle \frac{2}{3}(1 - n) = 0.2 \)
\(1 - n = 0.3\)
\( \displaystyle n = 0.7 = \frac{7}{10} \)