Final answer:
The probability of a success outcome for a binomial random variable can be calculated using the formula P(x) = nCx * p^x * q^(n-x), where n is the number of trials, p is the probability of success, q is the probability of failure, and x is the number of successful outcomes.
Step-by-step explanation:
The probability of a success outcome for a binomial random variable can be calculated using the formula P(x) = nCx * p^x * q^(n-x), where n is the number of trials, p is the probability of success, q is the probability of failure, and x is the number of successful outcomes. In this case, the expected value (mean) is given as 30 and the variance as 20. To find the probability of a success, we can use the formula for the expected value: 30 = np. Therefore, n * p = 30. Since we are interested in finding the probability of a success, we can rewrite the equation as p = 30 / n. Substituting the variance (20) into the formula for variance, we get: 20 = npq. Since we know that p = 30 / n, we can substitute this into the equation and solve for q as q = (20 - 30^2 / n) / n. Now we have both p and q, and we can calculate the probability of a success outcome.