Question

If a binomial trial has a probability of success of 0.2, how many successes would you expect out of 6000 trials?

1) 2400
2) 3600
3) 1200

Answer 1

To find the expected number of successes in 6000 binomial trials with a success probability of 0.2, multiply the number of trials by the probability (6000 × 0.2), which equals 1200 expected successes.

Step-by-step explanation:

If a binomial trial has a probability of success of 0.2, and you want to determine the expected number of successes out of 6000 trials, you apply the formula for the expectation in a binomial distribution, which is μ = np. Here, n = 6000 trials, and p = 0.2, which is the probability of success on any given trial. When you multiply these together, you get:

Expected successes = 6000 × 0.2 = 1200

Therefore, out of 6000 trials, you would expect 1200 successes, making option 3) the correct answer.