Question

A Tesla plant receives shipment of Tesla Model Y cars from New York, California, Florida and Texas. In all, the plant received 123 cars with New Your sending 33, 10 from Florida and California sending 46 to the Tesla plant. Four times a car is selected at random from the plant, each time without replacement. Find the probability that

(a) all four cars came from the Texas factory

(b) The first 3 cars came from California and the last one from Florida

(c) none of the four selected came from New York.

Answer 1

Let N, C F and T denote the event that Tesla plant receives a shipment of Tesla Model Y cars from New York, California, Florida and Texas respectively.

Given: n(N) = 33, n(F) = 10, n(C) = 46 and n(Total) = 123 and thus n(T) = 123 - (33+10+46) = 34

By definition of probability,

Pr(Event) = No. of favorable events / Total No. of events

(a) Probability that all four cars came from the Texas factory

.

= 0.0051

In other words, since, the car selected is not replaced, the first car would be selected from 34 out of 123, 2nd would be from (34-1) = 3 from (123-1) = 122 etc. Hence,

= 0.0051

(b) The probability that the first 3 cars came from California and the last one from Florida

..........The 1st 3 cars from the group of 46 and the last car from the group of 10)

= 0.0042

(c) None of the four selected came from New York.

.........(Since the cars not from New York = 123 - 33 = 90)

= 0.2815