Questions: Assume the geometric distribution applies. Use the given probability of success p to find the indicated probability. Find P(3) when p=0.20. P(3)= (Round to five decimal places as needed.)

Solution Steps

We are given the probability of success \( p = 0.20 \) and we need to find the probability \( P(3) \), which represents the probability that the first success occurs on the 3rd trial.

The probability mass function for a geometric distribution is given by:

\[ P(k) = (1 - p)^{k - 1} \cdot p \]

Substituting the values \( p = 0.20 \) and \( k = 3 \):

\[ P(3) = (1 - 0.20)^{3 - 1} \cdot 0.20 \]

Calculating the components:

\[ P(3) = (0.80)^{2} \cdot 0.20 = 0.64 \cdot 0.20 = 0.128 \]

Final Answer