A fair die is thrown 4 times. If getting a prime number on the die is considered as a success, then the probability of getting no success at all is

Step-by-step solution

The possible outcomes when a fair die is thrown are 1, 2, 3, 4, 5, 6 . The prime numbers on a die are 2, 3, 5 . Probability of getting a prime number (success) in a single throw is p = 3 6 = 1 2 . Probability of not getting a prime number (failure) in a single throw is q = 1 - p = 1 2 . The die is thrown 4 times, so n = 4 . The probability of getting no success at all ( 0 successes) is given by the binomial distribution: P(X = 0) = ⁴C₀ p⁰ q⁴ P(X = 0) = 1 ( 1 2 )⁰ ( 1 2 )⁴ = 1 16 Answer: 1 16