Question

A local dealer has two video stores in two locations. The Foothill Drive store does 70% of the dealer's business, and the Grand Avenue store does the rest. In the Foothill Drive store, 40% of all rentals are DVDs. At the Grand Avenue store, 30% of all rentals are DVDs. If a customer is selected at random, what is the probability that she will rent a DVD?

Options:
A) 0.28
B) 0.30
C) 0.36
D) 0.70

Answer 1

The overall probability of a customer renting a DVD from either the Foothill Drive or Grand Avenue store is 37%, taking into account the business share and DVD rental rate of each store. Based on the options given, none matches exactly, but option C (0.36) is the closest.

Step-by-step explanation:

The question asks to calculate the probability of renting a DVD from a local dealer that has two video stores, one on Foothill Drive and the other on Grand Avenue. We know that the Foothill Drive store does 70% of the business and has a 40% DVD rental rate. The Grand Avenue store does the remaining 30% of the business with a 30% DVD rental rate.

To solve this problem, we use the law of total probability:

1. Calculate the probability of renting a DVD at the Foothill Drive store: 70% business share × 40% DVD rental rate = 0.70 × 0.40 = 0.28.
2. Calculate the probability of renting a DVD at the Grand Avenue store: 30% business share × 30% DVD rental rate = 0.30 × 0.30 = 0.09.
3. Add these probabilities together to get the total probability of renting a DVD: 0.28 (Foothill) + 0.09 (Grand Avenue) = 0.37.

The most appropriate probability of renting a DVD when visiting either store is 37%. If forced to choose the closest option, it would be Option C, which is 0.36, closest to the calculated probability albeit slightly less.