Question

.  Rubber Tire Company has determined that their tires last 80,000 kilometres 95% of the time before the tread wears out, or they otherwise fail. If a tire fails at less than 80,000 km, the company provides a prorated refund.

1. If you purchase 4 tires, what is the probability that all four tires will last 80,000 km?
2. What is the likelihood that you will get a refund?
3. What is the likelihood that all of your tires will fail?

You are putting together a four person team for a business competition.  Your class is made up of 15 men and 12 women and team members will be selected at random.

            a.  What is the probability that the team will be all women?

            b. What is the probability that the team will be 2 mean and 2 women?

            c. What is the probability that the team will be all men?

Note: Once a person is picked, they cannot be picked again.

Answer 1

Question 1

Here Probability that a tire wears survives till 80000 km = 0.95

(a) We purchase four tires,

P(All four tire will survive 80000 km) = 0.95⁴ = 0.8145

(b) P(We will get a refund) = 1 - P(No Tire Fails) = 1 - 0.8145 = 0.1855

(c) P(All tire would fail before 80000 km) = (1- 0.95)⁴ = 0.00000625

Question 2

There are 15 men and 12 women

.Fourt person to be selected.

(a) P(Team would be all women) = ¹²C₄/²⁷C₄ = 0.0282

(b) P(2 men and 2 women) = ¹⁵C₂¹²C₂/ ²⁷C₄ = 0.3949

(c) P(Team will be all men) = ¹⁵C₄/²⁷C₄  = 0.0778