Question

An binomial probability experiment is conducted with the given parameters. Compute the probability of x successes in the n independent trials of the experiment n= 10, p= 0.9, x= 9

Answer 1

The probability of 9 successes in 10 trials in the binomial probability experiment is 0.387

Explanation:

In this question, we are asked to compute the probability of 9 successes in 10 trials , given that the probability of success is 0.9

Firstly we need to know which approach we are going to use to solve this problem. To compute this probability, the approach to use is the Bernoulli approximation. To use this, we need to know the probation failure.

We can represent this by let’s say q. The probability of failure q in this case is 1-p = 1-0.9 = 0.1

Let us figure out the Bernoulli expression here. It would look like;

nCx * p^x * q^(n-x)

Let’s impute the value properly, we have;

10C9 * 0.9^9 * 0.1^1

= 10 * 0.9^9 * 0.1 = 0.387