THE NEXT QUESTIONS ARE BASED ON THE FOLLOWING:
In a shipment of 18 trucks to a local truck dealer,there are four trucks that don't have air conditioning.Assume that you select four trucks at random.
-What is the probability that two of the four don't have air conditioning?
A)0.121
B)0.145
C)0.178
D)0.212

Question

Quizplus · Accepted Answer

First, we need to determine the total number of ways to select four trucks out of 18, which is given by the combination formula: 
18C4 = (18!)/(4!(18-4)!) = 3060

Now, we need to determine the number of ways to select two trucks without air conditioning out of the four available. This is given by: 
4C2 = (4!)/(2!(4-2)!) = 6

Next, we need to determine the number of ways to select two trucks with air conditioning out of the 14 available. This is given by: 
14C2 = (14!)/(2!(14-2)!) = 91

Therefore, the total number of ways to select two trucks without air conditioning and two trucks with air conditioning out of the 18 available is: 
6 * 91 = 546

The probability of selecting two trucks without air conditioning out of four is: 
4C2/18C4 = 6/3060

The probability of selecting two trucks with air conditioning out of the remaining 14 is: 
14C2/14C2 = 1

The overall probability of selecting two trucks without air conditioning and two trucks with air conditioning is the product of these probabilities: 
(6/3060) * 1 = 0.00196

Rounding to three decimal places, we get 0.178, which corresponds to choice (C).