A car dealer has 100 cars to sell on his lot. You are interested in buying a car

Question

A car dealer has 100 cars to sell on his lot. You are interested in buying a car from him, but you have been told that K of the cars on the lot are "lemons" (i.e. these cars have mechanical faults that are not apparent until you drive them). You are given information that K can be any of the 5 values {0,1,2,3,4}, and that all of these values are equally likely. What is the probability that there are less than 3 lemons on the lot? You decide to test drive 20 cars, selected at random from the lot. All 20 cars drive perfectly - i.e. none are lemons. Having determined that there are no lemons among the 20 randomly selected test cars, now what is the probability that there are less than 3 lemons on the lot? (Hint: for this part, consider the sample space to consist of all outcomes consistent with the fact that the 20 test cars are not lemons, for all possible values of K.)

Explanation / Answer

probability of each of {0,1,2,3,4] is equal.

Hence Probability of any one of them = 1/5 = 0.2

a> thus probability of less than 3 lemons = P(0) + P(1) + P(2) = 3*0.2 = 0.6

probability of less than 3 lemons is 60% = 0.6

b> Since there are no lemons in the 20 test - driven cars, probability still remains same for each of {0,1,2,3,4} = 1/5 = 0.2

Hence probablility of less than 3 lemons = 60% = 0.6

Related Questions

Navigate

• Browse (All)
• Browse A
• Subjects

---

---

Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.