Question

A car dealer sells 3 types of cars. It sells 50% of type X, 30% of type Y, and 20% of type Z. 91% of type X, 95% of type Y, and 97% of type Z have AC. If a car is selected randomly, find the probability it has no AC.

(a) 0.01
(b) 0.05
(c) 0.09
(d) 0.15

Answer 1

To find the probability that a randomly selected car has no AC, calculate the probabilities for each car type not having AC and sum them. The resulting probability is approximately 0.07, closest to option (c) 0.09.

Step-by-step explanation:

The subject of the given question is probability, which is a branch of mathematics that deals with the likelihood of events occurring. To find the probability that a randomly selected car has no air conditioning (AC), we can use the following steps:

1. Firstly, calculate the probability of selecting a car that does not have AC for each type:

• Type X without AC: 0.50 * (1 - 0.91) = 0.50 * 0.09 = 0.045
• Type Y without AC: 0.30 * (1 - 0.95) = 0.30 * 0.05 = 0.015
• Type Z without AC: 0.20 * (1 - 0.97) = 0.20 * 0.03 = 0.006

1. Add up the probabilities calculated in the previous step to get the total probability that a car has no AC: 0.045 + 0.015 + 0.006 = 0.066.
2. The probability is then approximately equal to 0.07, when rounded to two decimal places.

Therefore, the probability that a randomly selected car has no AC is closest to option (c) 0.09.