The traffic that makes a left turn at an intersection consists of two types of v
ID: 3127737 • Letter: T
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
the lane can accomodate 8 of B and 4 of A
A = 2B
SAMPLE SPACE = {(4A,8B,(6B1A),(4B2A),(2B3A),(1B,3A),(3B,2A),(5B1A),1A,2A,3A,4A,1B,2B,3B,4B,5B,6B,7B,8B}
1) ATLEAST ONE OF A = {(1A,2A,3A,4A,1A1B,1A2B,1A3B,1A4B,1A5B,1A6B,2A1B,2A2B,2A3B,2A4B,3A1B,3A2B)} THIS MEANS THAT MINIMUM ONE OF TYPE A IS THERE FOR LEFT TURN BUT THE LANE CAN BE OCCUPIED BY OTHER COMBINATIONS
2)TWO OF TYPE B = {2B,2B1A,2B2A,2B3A}
THIS MEAN THAT ON THE LANE THERE MUST BE ONLY TWO OF TYPE B SHOULD BE THR WITH OTHER COMINATIONS
3) EXACTLY ONE OF TYPE A AND PNE OF TYPE B = {1A1B} THIS MEANS ONLY TWO VEHICLES ARE THERE WITH BOTH OF ONE OF EACH TYPE.
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