Question

URGENT

Please help
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.
P(X≥3), n=7, p=0.1

Answer 1

We can use the binomial probability formula to solve this problem.

P(X≥3) = 1 - P(X<3)

First, we need to find P(X<3), which means finding the probability of getting 0, 1, or 2 successes in 7 trials with a probability of success of 0.1.

P(X<3) = P(X=0) + P(X=1) + P(X=2)

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

P(X=0) = (7 choose 0) * 0.1^0 * 0.9^7 = 0.4783

P(X=1) = (7 choose 1) * 0.1^1 * 0.9^6 = 0.3830

P(X=2) = (7 choose 2) * 0.1^2 * 0.9^5 = 0.1144

P(X<3) = 0.4783 + 0.3830 + 0.1144 = 0.9757

P(X≥3) = 1 - P(X<3) = 1 - 0.9757 = 0.0243

Therefore, the probability of getting at least 3 successes in 7 trials with a probability of success of 0.1 is 0.0243.