EXAMPLE 3.1.8

Gomer has to take a 5 question true/false quiz, but he hasn't studied. He will guess at each problem. In how many different ways is it possible to answer the quiz questions?

SOLUTION

When Gomer randomly answers the five questions, he makes five decisions.

i. Choose "True" or "False" as answer for first question: 2 options;

ii. Choose "True" or "False" as answer for second question: 2 options;

iii. Choose "True" or "False" as answer for third question: 2 options;

iv. Choose "True" or "False" as answer for fourth question: 2 options;

v. Choose "True" or "False" as answer for fifth question: 2 options.

According to the Fundamental Counting Principle the number of outcomes is

(2)(2)(2)(2)(2) = 32

How likely is it that he will get a score of 100%?

Since there are 32 different ways to answer the five questions, and only one of those 32 ways will match the key to quiz, the likelihood that he will get a 100% by guessing is "1 in 32." In other words, if there were 32 students taking the quiz, and every student guessed at every question, it would be reasonable to expect that one person would get a 100%. It would be unreasonable to expect a large number of the students to get scores of 100%.