The traffic that makes a left turn at an intersection consists of two types of v

Question

The traffic that makes a left turn at an intersection consists of two types of vehicles, types A and B. A type A vehicle is twice the length of type B. The left-turn lane can accomodate eight vehicles of Type B, four of type A, or combinations of A and B. Define the sample space of all possible combinations of vehicles waiting for a left turn at the intersection. Also, define the following evetns: (1) at least one vehicle of type A waiting for a left turn, (2) two vehicles of type B waiting for a left turn, and (3) exaclty one of type A and one of type B waiting for a left turn.

Explanation / Answer

Sample Space = {AAAA,AAABB,AABBBB,ABBBBBB,BBBBBBBB}

since it can contain either all A or 3A,2B or 2A,4B, or 1A,6B or all B's

(i) at least one vehicle of type A waiting for left turn

Set of Possible samples = {AAAA,AAABB,AABBBB,ABBBBBB}

(ii) two vehicles of type B waiting for left turn

Set of possible spaces = {3A,2B}

(iii) No sample outcome, there must be more than one of A and one of B

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