Question

In a town of $6000$ people, $1200$ are over $50$ years old and $2000$ are females. It is known that $30\%$ of the females are over $50$ years. What is the probability that a randomly chosen individual from the town is either female or over $50$ years?

• A. $\frac{13}{30}$
• B. $\frac{15}{30}$
• C. $\frac{15}{31}$
• D. $\frac{17}{31}$

Answer 1

Answer: (A)

Let $ E_1 =$ event of person being a female,
and $E_2 =$ event of person being $50$ years old.
Then, $n(E_1) = 2000, n(E_2) = 1200$, and $n(E_1 \cap E_2) = (30\%$ of $2000) = 600$.
Now, $n(E_1 \cup E_2) = n(E_1) + n(E_2) - n(E_1 \cap E_2) = 2600$.
$\therefore P(E_1 \cup E_2) = \frac{2600}{6000} $
$= \frac{13}{30}$.