Question

Two events $X$ and $Y$ are such that $P(X) = \frac{1}{3}$, $P(Y) = n$, and the probability of occurrence of at least one event is 0.8. If the events are independent, then the value of $n$ is:

• A. $\frac{3}{10}$
• B. $\frac{1}{15}$
• C. $\frac{7}{10}$
• D. $\frac{11}{15}$

Answer 1

Answer: (C)

$\frac{7}{10}$

Answer 2

For independent events $X$ and $Y$, the probability of at least one occurring is given by:

$P(X \cup Y) = P(X) + P(Y) - P(X)P(Y).$

Substituting the given values:

$0.8 = \frac{1}{3} + n - \left(\frac{1}{3}\right)n.$

Simplifying:

$0.8 = \frac{1}{3} + n - \frac{n}{3}.$

Combining terms:

$0.8 = \frac{1}{3} + \frac{2n}{3}.$

Multiplying the entire equation by 3:

$2.4 = 1 + 2n.$

Rearranging:

$2n = 1.4 \implies n = 0.7 = \frac{7}{10}.$