Akilah owns a used car lot, which has 25 compacts, 35...

Akilah owns a used car lot, which has 25 compacts, 35 sedans, and 29 trucks for sale. Some of the vehicles have an upgraded trim package: 11 of the compacts have luxury trim, 19 of the sedans have luxury trim, and 9 of the trucks have luxury trim. (Give each result accurate to at least 3 decimal places.) a. A vehicle is selected from the lot at random. What is the probability that it will be a compact or a truck? b. A vehicle is selected from the lot at random. What is the probability that it will be a sedan, or that it will have luxury trim? c. Two vehicles are selected from the lot at random. What is the probability that the first one will be a compact and the second will be a sedan?

Transcript

00:01 We are given a vehicle types sold and the associated probabilities for the same.

00:08 So the vehicle types are pc which represents passenger car, pt which represent pickup truck, suv and co which denotes crossover and minivaned by mv.

00:30 The associated probabilities are 0 .46 .15, 0 .10.

00:40 This probability is unknown and 0 .05.

00:45 So in the first case, we need to find the probability of crossover cars.

00:50 This is equal to 1 minus probability of passenger car minus probability of pickup truck, minus probability of suv, minus probability of minivan.

01:08 This is equal to 1 minus 0 .46 minus 0 .15 minus 0 .10 minus 0 .05.

01:18 This is equals to 0 .24.

01:22 Hence the probability of crossover card is 0 .24.

01:29 Now how do we know this probability of crossover? this is known because in any probability distribution the summation of probabilities is always equals to 1.

01:44 So using this formula we know the probability of crossover car and applying this we get the probability at point two four now in the next question we have to find the probability of pickup truck of the vehicle being pickup truck given that it is not a passenger car not a passenger car not a passenger car is denoted by p c to the power c which is complement of passenger car so using the conditional probability formula we write probability of pickup truck intersection it is not a passenger car divided by probability of passenger car not being a passenger car so if it is not a passenger car and we have to see it is a pickup truck so intersection of this will result into probability of pickup truck and this can be written as one minus probability of passenger car replacing the values 0 .15 divided by 1 minus 0 .46...

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