Question

The jackson family is undecided about whether or nara buy a new car of the

Answer 1

The question is incomplete. The complete question is :

The Jackson family is undecided about whether or not to buy a new car. If the probability is .9 that they will buy one, and if the probability is .3 that they will buy a Ford, and if the probability is .4 that they will purchase a car getting more than 20 miles per gallon, what is the probability that they will buy either a car getting more than 20 miles per gallon or a Ford, if all Fords get more than 20 miles per gallon?

Solution :

Given that :

The probability of buying a new car,  $P(NC) = 0.9$

Probability of buying Ford = 0.3

That is, if Jackson family buy a car that is a ford car, $P(F) = 0.9 \times 0.3$

                                                                                                = 0.27

The probability for getting more than 20 miles per gallon = 0.4

That is if Jackson family buy a car that have more than 20 miles per gallon mileage, $P(20) = 0. 9 \times0.4=0.36$

The conditions

All of the car have more than 20 miles per gallon mileage.

It means that buying a ford car is subset of getting more than 20 miles per gallon.

$P(20 \text{ miles per gallon}\ \cap \ \text{Ford})=P(F)$

Therefore, the probability of buying a car either getting more than 20 miles per gallon or ford = $P(20 \text{ miles per gallon}\ \cup \ \text{Ford})$

Therefore,

$P(20 \text{ miles per gallon}\ \cup \ \text{Ford})=P(20) + P(F) - P(20 \text{ miles per gallon }\cap \ \text{Ford})$

$P(20 \text{ miles per gallon}\ \cup \ \text{Ford})=P(20) + P(F) - P(F)$

$P(20 \text{ miles per gallon}\ \cup \ \text{Ford})=P(20)$

                                                = 0.36

Thus the probability that Jackson family is buying a car either getting more than 20 miles per gallon or ford is 0.36