Question

A bag contains $17$ tickets numbered $1$ to $17$. A ticket is drawn and replaced, then one more ticket is drawn and replaced. Probability that first drawn number is even and second is odd, is

• A. $\frac{81}{289}$
• B. $\frac{72}{289}$
• C. $\frac{64}{289}$
• D. none of these

Answer 1

Answer: (B)

$\frac{72}{289}$

Let $A$ be the event that first drawn number is even and $B$ be event that the second number drawn number is odd.

Total number of even numbers $=\left[\frac{17}{2}\right]=8$

$\Rightarrow P\left(A\right)=\frac{8}{17}$ and $P\left(B\right)=\frac{9}{17}\Rightarrow P(A\cap B)=\frac{72}{289}$