Simons Chocolate factory creates colour coated chocolate candies. A small box contains 20 candies. There are four possible colours for the coating.

Question

The colour of candies in every box is: 8 red, 4 orange, 6 blue and 2 green. what is the expected number of red candies you will eat?

Answer 1

In probability, expected value is a measure of weighted average that tells you the long-term expected outcome of a random variable. For example, say that the expected value of buying a raffle ticket for a raffle is $-1. This means that if we were to keep entering into the raffle over and over again, we would expect on average $1 lost at the end. A random variable is a variable whose value are assigned to the outcomes in an experiment. Our random variable in this case is red candies; it's a variable because over the course of eating candies the outcome of eaten red candies will vary.

Expected value is calculated as follows: E(x) = Σ x * P(x). E(x) is the expected value, x is the outcome value, and P(x) is the probability that the outcome occurs. The summation sign is used to sum the products of outcome value and probability for all possible outcomes that can occur in the experiment. In this problem, we are only interested in the outcome of red candy so we will neglect the summation sign. We have 20 total candies which is our outcome value x with an 8/20 or 2/5 = 0.4 chance of picking a red candy which is our probability value P(x).

So, expected value is:

E(x) = (20)*(0.4) = 8. This means that if we were to keep buying boxes of candy, randomly picking 1 candy to eat per box, we would expect on average 8 total red candies to be eaten in the end. Hope this helps.