A and B are participating in the same contest; the probability of their winning are $\frac{5}{9}$ and $\frac{1}{4}$ respectively. What is the probability that neither of them will win the contest?

$\frac{1}{3}$

The correct answer is Option (4) → $\frac{1}{3}$

Interpret the given probabilities as fractions:

• Probability that A wins = $\frac{5}{9}$​
• Probability that B wins = $\frac{1}{4}$​

Step 1: Probability that A does not win

$1 - \frac{5}{9} = \frac{4}{9}$​

Step 2: Probability that B does not win

$1 - \frac{1}{4} = \frac{3}{4}$​

Step 3: Probability that neither A nor B wins

$\frac{4}{9} \times \frac{3}{4} = \frac{12}{36} = \frac{1}{3}$