What is the probability that the Toyota leaves first?

Question

Assume that there are 8 cars: 2 Chevrolets, 5 Fords, and 1 Toyota. Two cars leave at random, one after the other. Draw a tree diagram and use it to answer the following questions.
(1) What is the probability that the Toyota leaves first?

(2) What is the probability that the two cars which leave are Chevrolets?

(3) What is the probability that the Toyota is the second car to leave?

(4) What is the probability that the Toyota is the second car to leave given that one of the two cars is the Toyota?

(5) What is the probability that a Ford is the last to leave given that the Toyota leaves first?

Answer 1

"Two cars leave at random"

 

for the first car to leave, there are 8 possibilities.   After that, there are 7 possibilities for the 2nd car.

 

1)  There is only 1 Toyota, so the prob. of it leaving first is 1/8

 

2)  prob of #1 being Chevrolet = 2/8.  Prob. of #2 being Chev. = 1/7.  net probability = 2/8 * 1/7 = 1/28

 

3)  first, the prob of something besides the Toyota going first is 7/8.  Next, there are 7 possibilities, one of which is the toyota.

net probability 7/8 * 1/7 = 1/8

 

4) If we know that the Toyota is either 1st or 2nd, then the prob of either is 1/2

 

5) If the Toyota leaves first, there are 7 choices for the 2nd.  There are 5 fords, so p = 5/7

(Same answer for ANY car but a Ford going first)