About probability

Question

Consider a Bernoulli process with probability of success 0.7. What is the probability that there are 4 l’s and 3 O's in trials 36-42?

Answer 1

Using the binomial formula, C(7, 4).7⁴(1-.7)^7-4 = 35 * .2401 * .027 = .2269

Alternatively, you can use a calculator or Excel and enter the appropriate values for p, the number of trials, and the number of successes.

For example, in Excel, binom.dist(4, 7, .7, 0) = .2269

Note: the final 0 means that we want P(X = 4), not P(X <= 4).1 gives the latter value.