### Video Transcript

In a binomial experiment, the probability of success in each trial is 0.2 and 40 trials are performed. Let π be the random variable, which counts the number of successes. Find the variance of π.

Letβs firstly look at the two key properties of a binomial experiment. Firstly, it consists of π repeated independent trials. There are only two possible outcomes from each trial: success and failure. A binomial experiment has two key values denoted by π and π. π is the number of trials and π is the probability of success.

In this particular question, the value of π is 40 and the value of π is 0.2. When dealing with a binomial experiment, the mean denoted by πΈ of π, the expected value, is equal to π multiplied by π. The variance, or Var of π, is equal to π multiplied by π multiplied by one minus π. In this question, the variance is equal to 40 multiplied by 0.2 multiplied by 0.8. This is equal to 6.4.

A binomial experiment with 40 trials and probability of success of 0.2 has a variance of 6.4.