Question Video: Calculating the Mean of a Binomial Distribution

Video Transcript

In a binomial experiment, the probability of success in each trial is 0.3 and 20 trials are performed. What is the expected number of successful trials?

Let’s begin by recalling the two key properties of a binomial experiment. A binomial experiment consists of 𝑛 independent repeated trials. There are two possible outcomes to each trial: success and failure. This means that any binomial experiment has two key values, denoted by 𝑛 and 𝑝. 𝑛 is the number of trials and 𝑝 is the probability of success.

In this question, we’re told that there are 20 trials and the probability of success is 0.3. Therefore, 𝑛 equals 20 and 𝑝 equals 0.3. The expected value or mean denoted by 𝐸 of 𝑥 is equal to 𝑛 multiplied by 𝑝. In this question, we need to multiply 20 by 0.3. 0.3 multiplied by 10 is equal to three. And multiplying this by two gives us six. The expected number of successful trials in an experiment with 20 trials and probability of success of 0.3 is six.

We know that 0.3 is equal to 30 percent. This means we would expect a successful outcome 30 percent of the time. We could calculate 30 percent of 20. One way of doing this is to find 10 percent and multiply the answer by three. Either way, our final answer is six.