Question

Johnny finds that the probability of a gaming system having a defect is 12%. What is the probability that the first system Johnny finds with a defect is the 9th on he tests?

a) 0.043
b) 0.093
c) 0.388
d) 0.087

Answer 1

The probability that the first gaming system Johnny finds with a defect is the 9th one is 0.087.

Step-by-step explanation:

To find the probability that the first gaming system Johnny finds with a defect is the 9th one, we can use the geometric distribution. The probability of finding a defective gaming system is 0.12 (12%).

Using the formula for the probability of a geometric distribution, where p is the probability of success and x is the number of trials, we can calculate:

P(x = 9) = (1 - p)^(x-1) * p = (1 - 0.12)^(9-1) * 0.12 = 0.087

Therefore, the probability that the first gaming system Johnny finds with a defect is the 9th one is 0.087.