Question

Let $S = \{2,\,5,\,8,\,11,\,14,\,17,\,20,\,23\}$. Two integers $m,\,n$ are chosen one by one from $S$ with replacement. Then the probability that $mn$ is odd, is

• A. $\dfrac{3}{4}$
• B. $\dfrac{3}{7}$
• C. $\dfrac{3}{5}$
• D. $\dfrac{3}{7}$
• E. $\dfrac{3}{5}$

Hint:

For the product $mn$ to be odd, both $m$ and $n$ must be odd. Count odd elements in the set carefully. Since the selection is with replacement, draws are independent, so multiply the individual probabilities.

Answer 1

The Correct Option is B