Question

The accompanying table shows the number of cars of two different brands sold at a dealership during a certain month. The number of coupes and sedans is also shown.VehicleCoupeSedanTotalBrand 175240315Brand 226570335Total340310650If one of these vehicles is selected at random, determine the probability that it was a coupe, given that the vehicle selected was Brand 1.The probability that a vehicle was a coupe, given that it was Brand 1, is(Round to four decimal places as needed.)

Answer 1

We are given a two-way probability table.

We are asked to find the conditional probability that it was a coupe, given that the selected vehicle was Brand 1.

P(coupe | Brand 1) = ?

Recall that the conditional property is given by

`P(coupe|Brand\: 1)=\frac{P(coupe\: and\: Brand\: 1)}{P(Brand\text{ 1)}}`

From the given table we see that,

`\begin{gathered} P(coupe\: and\: Brand\: 1)=75 \\ P(Brand\: 1)=315 \end{gathered}`

So, the probability is

`\begin{gathered} P(coupe|Brand\: 1)=\frac{P(coupe\: and\: Brand\: 1)}{P(Brand\text{ 1)}} \\ P(coupe|Brand\: 1)=(75)/(315) \\ P(coupe|Brand\: 1)=0.2381 \end{gathered}`

Therefore, the probability that a vehicle was a coupe, given that it was Brand 1, is found to be 0.2381