Question

Consider a geometric probability distribution

with p = 0.85, and x be the number of trial in
which the first success occurs
(a) Find P (x = 4)

Answer 1

To find P(x = 4) in a geometric probability distribution with p = 0.85, use the formula P(x = k) = (1 - p)^(k-1) * p. Substituting the values, P(x = 4) = 0.03225.

Step-by-step explanation:

Geometric Probability Distribution

In this problem, we have a geometric probability distribution with p = 0.85, where x represents the number of trials until the first success occurs.

To find P(x = 4), we can use the formula for the probability mass function of a geometric distribution: P(x = k) = (1 - p)^(k-1) * p. Substituting the values, we get P(x = 4) = (1 - 0.85)^(4-1) * 0.85.

P(x = 4) = 0.15^3 * 0.85 = 0.03225.