Question

If the probability of success is .30, what is the probability of obtaining the first success within the first five trials

Answer 1

To calculate the probability of obtaining the first success within the first five trials when the probability of success is 0.30, we can use the geometric probability formula.

Step-by-step explanation:

This is a geometric problem because there may be a number of failures before the first success is obtained within the first five trials. In this case, the probability of success is 0.30 for each trial.

To find the probability of obtaining the first success within the first five trials, we can use the formula:

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

where P(X = k) is the probability of getting the first success on the kth trial, p is the probability of success, and k is the number of trials.

In this case, k can take on the values 1, 2, 3, 4, or 5. So we need to calculate:

P(X = 1) + P(X = 2) + P(X = 3) + P(X = 4) + P(X = 5)

Answer 2

The probability of NOT obtaining success within the first trial is (1-0.3)=0.7
The probability of NOT obtaining success within the first five trials is
=0.7^5=0.16807

The probability of obtaining ANY success within the first five trials
=1-(0.7^5)=0.83193