Question

A particular experiment is successful one out of every eight times it is run. Let n be the minimum number of times the experiment must be run to have more than a 60% chance of a successful outcome. Then n is the smallest positive integer that satisfies which ONE of the following inequalities?

(7/8)> 60/100
(7/8)<60/100
1/8<40/100
7/8<40/100
1/8<60/100

Answer 1

The minimum number of times the experiment must be run to have more than a 60% chance of a successful outcome is n > 4.

Step-by-step explanation:

Let X be the number of successful outcomes in the experiment. The probability of a successful outcome in each trial is p = 1/8. The probability of a failure outcome in each trial is q = 1 - p = 7/8.

We need to find the minimum number of trials, n, such that the probability of having more than a 60% chance of a successful outcome is greater than 60/100.

The probability of having x successful outcomes in n trials is given by the binomial distribution formula: P(X = x) = (nCx) * p^x * q^(n-x), where nCx represents the number of ways to choose x successes from n trials.

In this case, we want to find the smallest n that satisfies the inequality: Σ[P(X = x)] > 60/100. This means we need to calculate the cumulative sum of probabilities for x = 1 to n and check if it is greater than 60/100.

The smallest positive integer n that satisfies this inequality is 4, since the cumulative sum of probabilities for x = 1 to 4 is larger than 60/100.