Question

examples 2 and 3

1. awards the student of the month gets to choose one award from 9 gift certificates to area restaurants, 8 t - shirts, 6 water bottles, or 5 gift cards to the mall. what is the probability that the student of the month chooses a t - shirt or a water bottle?

Explanation:

Step1: Find total number of awards

To find the total number of awards, we sum up the number of each type of award. The number of gift certificates is 9, T - shirts is 8, water bottles is 6, and mall gift cards is 5. So the total number of awards \( n = 9 + 8+6 + 5\)
\(n=28\)

Step2: Find number of T - shirts or water bottles

The number of T - shirts is 8 and the number of water bottles is 6. Since choosing a T - shirt and choosing a water bottle are mutually exclusive events (a student can't choose both a T - shirt and a water bottle at the same time), the number of ways to choose a T - shirt or a water bottle \(m=8 + 6\)
\(m = 14\)

Step3: Calculate the probability

The probability \(P\) of an event is given by the formula \(P=\frac{\text{Number of favorable outcomes}}{\text{Total number of outcomes}}\). Here, the number of favorable outcomes (choosing a T - shirt or a water bottle) is 14 and the total number of outcomes is 28. So \(P=\frac{14}{28}\)
Simplifying the fraction \(\frac{14}{28}=\frac{1}{2}\)

Answer:

\(\frac{1}{2}\)