A Toyota dealership is trying to decide on a 10 car lineup t

A Toyota dealership is trying to decide on a 10 car lineup to display along the road and entice customers to come in. They have 50 different cars from which to choose: 5 product lines (Prius, Camry, Corolla, Tundra, Rav4), and 10 different models or colors of each.

(a) The manager assigns the task to a lazy employee who just sticks 10 random cars out front. What is the chance that all 10 cars were among the 20 sedans (Camrys and Corollas)?

(b) What is the chance that they’re all sedans + Prius (Camry / Corolla / Prius) or all large vehicles + Prius (Rav4 / Tundra / Prius)? Note: So no Tundra if there’s a Corolla, and you will have only one answer like “A 4%+3%+3% = 10% chance of this because ...”

(c) My wife and I walk into the dealership with plans to buy two cars, one for each of us. There’s a 60% chance I’ll choose a Prius and a 30% chance she’ll choose a Tundra. If our choices are made independently then what is the chance that I get a Prius and she decides not to get a Tundra?

Solution

(a) The manager assigns the task to a lazy employee who just sticks 10 random cars out front. What is the chance that all 10 cars were among the 20 sedans (Camrys and Corollas)?

10 / 50 = 0.2

(b) What is the chance that they’re all sedans + Prius (Camry / Corolla / Prius) or all large vehicles + Prius (Rav4 / Tundra / Prius)? Note: So no Tundra if there’s a Corolla, and you will have only one answer like “A 4%+3%+3% = 10% chance of this because ...”

5 / 10 * 10 / 20 = 0.25

(c) My wife and I walk into the dealership with plans to buy two cars, one for each of us. There’s a 60% chance I’ll choose a Prius and a 30% chance she’ll choose a Tundra. If our choices are made independently then what is the chance that I get a Prius and she decides not to get a Tundra?

0.50 - 0.30 = 0.20