X and Y are two independent event. If $P(X) = \frac{1}{5}$ and $P(X \cap Y) = \frac{2}{15}$, find $P(Y)$.

Assessment: WAEC SSCE - Further Mathematics - 2007 (Objective) Subject: Further Mathematics

Question 1 Report

$\frac{2}{3}$

$\frac{2}{5}$

$\frac{1}{3}$

$\frac{1}{5}$

Answer Details

The formula to find the probability of the intersection of two independent events is given by: $$P(X \cap Y) = P(X) \times P(Y)$$ In this case, we know that: $$P(X) = \frac{1}{5}$$ $$P(X \cap Y) = \frac{2}{15}$$ Substituting the values into the formula, we have: $$\frac{2}{15} = \frac{1}{5} \times P(Y)$$ Solving for $P(Y)$, we get: $$P(Y) = \frac{\frac{2}{15}}{\frac{1}{5}} = \frac{2}{15} \times \frac{5}{1} = \frac{2}{3}$$ Therefore, the probability that event Y occurs is $\frac{2}{3}$. Answer: (a) $\frac{2}{3}$.

Read lesson note on Probability (WAEC)

Probability

View Answer

X and Y are two independent event. If \(P(X) = \frac{1}{5}\) and \(P(X \cap Y) = \frac{2}{15}\), find \(P(Y)\).

Download The App On Google Playstore

X and Y are two independent event. If \(P(X) = \frac{1}{5}\) and \(P(X \cap Y) = \frac{2}{15}\), find \(P(Y)\).

Related Questions

Download The App On Google Playstore