Solution Found!
Refer to Exercise 2.166. Let Y denote the actual quality
Chapter 2, Problem 167SE(choose chapter or problem)
Problem 167SE
Refer to Exercise 2.166. Let Y denote the actual quality rank of the best tire selected by the customer. In Exercise 2.166, you computed P(Y = 3). Give the possible values of Y and the probabilities associated with all of these values.
Reference
Eight tires of different brands are ranked from 1 to 8 (best to worst) according to mileage performance. If four of these tires are chosen at random by a customer, find the probability that the best tire among those selected by the customer is actually ranked third among the original eight.
Questions & Answers
QUESTION:
Problem 167SE
Refer to Exercise 2.166. Let Y denote the actual quality rank of the best tire selected by the customer. In Exercise 2.166, you computed P(Y = 3). Give the possible values of Y and the probabilities associated with all of these values.
Reference
Eight tires of different brands are ranked from 1 to 8 (best to worst) according to mileage performance. If four of these tires are chosen at random by a customer, find the probability that the best tire among those selected by the customer is actually ranked third among the original eight.
ANSWER:
Answer:
Step 1 of 1:
In this question, we are asked to find the possible values of and the probabilities associated with all of these values.
Eight tires of different brands are ranked from 1 to 8. If four of these tires are chosen at random by a customer, find the probability that the best tire among those selected by the customer is actually ranked third among the original eight.
Given 8 number of tires which is ranked from best to worst, and from these tires, four of these tires are chosen by a customer.
Here we can apply the combination theorem,
The number of unordered subsets of size chosen (without replacement) from
available object is
……………..(1)
A number of ways by which we can randomly choose 4 tires from 8 tires is,
[using equation (1)]
If the best tire the customer has is ranked to third, the other three tires are from ranks 4, 5, 6, 7 and 8.
Let be the event of choosing the best tire.