In a series of 5 independent Bernoulli trials, the probability of exactly 1 success equals the probability of exactly 2 successes. The probability of success (p) in a single trial is:

In a series of 5 independent Bernoulli trials, the probability of exactly 1 success equals the probability of exactly 2 successes. The probability of success (p) in a single trial is:

• A. 1/2
• B. 1/3
• C. 1/4
• D. 2/3

Answer: B) 1/3

Explanation: ⁵C₁ p¹ q⁴ = ⁵C₂ p² q³ → 5pq⁴ = 10p²q³. Dividing by 5pq³ (assuming p,q > 0) gives q = 2p. Since p+q=1, p+2p=1, 3p=1, so p=1/3.