Question

An experiment consists of 400 observations and four mutually exclusive groups. If the probability of a randomly selected item being classified into any of the four groups is equal, then the expected number of items that will be classified into group 1 is ________.

Answer 1

Answer:

The expected number of items that will be classified into group 1 is 100.

Step-by-step explanation:

For each observation, there are only two possible outcomes. Either it will be classified into group 1, or it will not. The probability of an observation being classified into group 1 is independent of any other observation, which means that the binomial probability distribution is used to solve this question.

Binomial probability distribution

Probability of exactly x successes on n repeated trials, with p probability.

The expected value of the binomial distribution is:

$E(X) = np$

400 observations

This means that $n = 400$

Four mutually exclusive groups. The probability of a randomly selected item being classified into any of the four groups is equal.

This means that $p = 0.25$

Then the expected number of items that will be classified into group 1 is

$E(X) = np = 400*0.25 = 100$

100 is the answer.