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, $n(E_1\cup E_2)=n(E_1)+n(E_2)-n(E_1\cap E_2)=2600$.
$\therefore P(E_1\cup E_2)=\frac{2600}{6000}$
$=\frac{13}{30}$.