Question

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Find the probability of exactly one successes in five trials of a binomial experiment in which the probability of success is 5%
round to the nearest tenth

Answer 1

We can use the formula for the probability mass function of a binomial distribution:

P(X = k) = (n choose k) * p^k * (1 - p)^(n-k)

Where:

n = number of trials

k = number of successes

p = probability of success

In this case, n = 5, k = 1, and p = 0.05. Plugging these values into the formula, we get:

P(X = 1) = (5 choose 1) * 0.05^1 * (1 - 0.05)^(5-1) ≈ 0.23

Rounding to the nearest tenth, the probability of exactly one success in five trials with a 5% probability of success is approximately 0.2 or 20%.

Explanation: