Exercise 9 Page 772

We want to describe both a nearly certain and a highly unlikely event in a real-world situation. To do so, let's consider a wedding reception with 100 adult guests.

Studies claim that about 10 % of the worldwide human population is left-handed. Let's assume that the sample at the wedding is unbiased. Therefore, the probability that a random person at the wedding is left-handed is about 10 %. P(Person is left-handed) = 10 % = 0.1 Now, consider event A that every adult guest at the wedding is left-handed. Since each person has only 10 % chance of being left-handed, it is highly unlikely for every person to have this trait. Therefore, the probability of this event is close to 0. P(A) ≈ 0 Alternatively, consider the event that at least one person at the wedding is right-handed. Note that this event is the complement of the event that every person is left-handed.

The sum of the probabilities of an event and its complement is 1. P(A) + P(NotA) = 1 ⇕ P(NotA) = 1 - P(A) Because P(A) is close to 0, P(NotA) must be close to 1. Therefore, the probability that at least one person at the wedding is right-handed is nearly certain to occur.