Target Exam

CUET

Subject

-- Applied Mathematics - Section B2

Chapter

Probability Distributions

Question:

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:

Options:

1/3

1/729

728/729

665/729

Correct Answer:

665/729

Explanation:

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: $P(X \ge 1) = 1 - P(X=0)$

$P(X=0) = q^6 = \left(\frac{2}{3}\right)^6 = \frac{64}{729}$

$P(X \ge 1) = 1 - \frac{64}{729} = \frac{665}{729}$