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?
Answer & explanation
Correct answer: option 4
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
$\frac{4}{9} \times \frac{3}{4} = \frac{12}{36} = \frac{1}{3}$