I need help with this question Find the probability for (geometric distribution)

Question

I need help with this question Find the probability for (geometric distribution) p = 0.40. success occurs on trial n = 3 p = 0.75, success occurs on trial n = 5 p = 0.30, success occurs on trial n = 2 Find the probability for (Poisson distribution) Given n = 200, probability of success on a single trial p = 0.04, r = 8 successes Given n = 150, probability of success on a single trial p = 0.06, r lessthanorequalto 2 successes Determine the type of distribution for each and then solve. Susan is taking western civilization this summer on a pass/fail basis. The department teaching the course has a history of passing 77% of the students in western civilization each term. Let n = 1, 2, 3, ... representing the number of times a student takes western civilization until the first passing grade is received. What is the probability that Susan passes on the first try (n = 1) What is the probability that Susan passes on the second try (n = 2)? What is the probability that Susan needs three or more tries to pass? What is the expected number of attempts a student needs to pass the course?

Explanation / Answer

P(x = n) = p * q^(n - 1)

(a) p = 0.4, q = 1 - p = 0.6, n = 3

P(x = 3) = 0.4 * 0.6^(3 - 1) = 0.144

(b) p = 0.75, q = 1 - p = 0.25, n = 5

P(x = 5) = 0.75 * 0.25^(5 - 1) = 0.0029

(c) p = 0.3, q = 1 - p = 0.7, n = 2

P(x = 2) = 0.3 * 0.7^(2 - 1) = 0.21

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