Assume the random variable X has a binomial distribution with the given probability of obtaining a success. Find the following probability, given the number of trials and the probability of obtaining a success. Round your answer to four decimal places.

Question

P(X≥4)
, n=8
, p=0.4

Answer 1

To find P(X≥4) when n=8 and p=0.4, we can use the binomial probability formula:

P(X≥4) = 1 - P(X<4)

First, we can calculate P(X<4) by adding the probabilities of getting 0, 1, 2, and 3 successes:

P(X=0) = (8 choose 0) * (0.4)^0 * (0.6)^8 = 0.0016
P(X=1) = (8 choose 1) * (0.4)^1 * (0.6)^7 = 0.0126
P(X=2) = (8 choose 2) * (0.4)^2 * (0.6)^6 = 0.0477
P(X=3) = (8 choose 3) * (0.4)^3 * (0.6)^5 = 0.1147

Adding these probabilities together:
P(X<4) = 0.0016 + 0.0126 + 0.0477 + 0.1147 = 0.1766

Now, we can find P(X≥4) by subtracting this from 1:
P(X≥4) = 1 - 0.1766 = 0.8234

Therefore, the probability of P(X≥4) when n=8 and p=0.4 is 0.8234.