A family that owns two care (a new one and an old one) is selected; each of the

Question

A family that owns two care (a new one and an old one) is selected; each of the care could be manufactured either in America (U), Europe (K), or Asia (A). What are the possible outcomes of this experiment (sample space S)? Which outcomes are contained in the event that only one car is American? Which outcomes are contained in the event that the two care are made in Europe? What is the compliment of this event? Identify two events that are mutually exclusive. Now a car produced in Europe or Asia will be referred to as Foreign (F) car. Let A_1 = {the older car is American} and A_2 ={the newer car is American}, P (A_1) = 0.7, P(A2) = 0.5, and P(A_1 n A2) = 0.4. Write down the following (write down the outcomes): The space, S Event A_1={the older car is American} Event A_2={the newer car is American}. Write down the following events (which outcomes are contained in the event) AND calculate the associated probability (you should express the probability first as a function of A_1, A_2 and then find its value) The older car is Foreign The newer car is Foreign At least one car is American Both cars are foreign Exactly one of the two cars is American Calculate the probability that the older car is American given that the newer car is American

Explanation / Answer

Part A

(a)

There are total 3*3 = 9 outcomes in the sample. Following is the sampe space:

S = {UU, UE, UA, EU, EE, EA, AU, AE, AA}

First letter in each outcome shows the first car and second letter scond car.

(b)

The required outcomes are:

UA, EA, AE, AU

(c)

The required outcome is EE. Let this event shows by C. So the complment of this event is

C^c = {UU, UE, UA, EU, EA, AU, AE, AA}

(d)

Event "Both car are manufucatured in America" and event "Both car are manufactured in Europe" are mutually exclusive.

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