Decide if the following experiment is a binomial experiment. Drawing cards from a deck of 52 cards to see how many times the number five appears. If it is, state the probability of success as a fraction.
Let’s begin by defining a binomial experiment. This is an experiment with a fixed number of independent trials which only have two outcomes. These are usually written as success and failure. As the deck of cards has 52 cards, the fixed number of trials is 52. We are trying to see how many times the number five appears. Therefore, success will be drawing a five, failure will be not drawing a five. Therefore, there are only two outcomes, drawing a five and not drawing a five. We can, therefore, conclude that, yes, this is a binomial experiment.
We were also asked to calculate the probability of success. There are four fives in an ordinary deck of cards, the five of hearts, the five of diamonds, the five of clubs, and the five of spades. This means that four out of the 52 cards are fives. Both of these numbers can be divided by four. Four divided by four is equal to one. And 52 divided by four is equal to 13. The probability of success written as a fraction is one out of 13, or one thirteenth.