Question

Let x be a binomial random variable with n=10 and p=0.2 In how many possible outcomes are there exactly 8 successes?

Answer 1

There is a formula for the Binomial Density Function

Explanation:

Let n be the number of trials.
Let k be the number of successes at trial.
Let p be the probability of success at each trial.
Then the probability of succeeding at exactly k trials is
`(n!)/(k!(n-k)!)p^k(1-p)^(n-k)`
In this instance, n = 10, k = 8, and p = 0.2, so that

`p(8) = (10!)/(8!2!)(0.2)^8(0.8)^2`
`p(8) = 45(0.2)^8(0.8)^2`