A die is tossed 6 times and getting "1 or 5" is considered a success. The probability of getting at least one success in six tosses is:
Answer & explanation
Correct answer: option 4
The correct answer is Option (4) → 665/729
Probability of success in a single toss: $p = P(1 \text{ or } 5) = \frac{2}{6} = \frac{1}{3}$
Probability of failure: $q = 1 - p = \frac{2}{3}$
Number of trials: $n = 6$
Probability of at least one success: $P(X \ge 1) = 1 - P(X=0)$
$P(X=0) = q^6 = \left(\frac{2}{3}\right)^6 = \frac{64}{729}$
$P(X \ge 1) = 1 - \frac{64}{729} = \frac{665}{729}$