The joint probability distribution of the number X of cars and the number Y of b

Question

The joint probability distribution of the number X of cars and the number Y of buses per signal cycle at a proposed left-turn lane is displayed in the accompanying joint probability table p(x, y) 0 2 0 0.010 0.015 0.025 1 0.020 0.030 0.050 2 0.050 0.075 0.125 3 0.060 0.090 0.150 4 0.040 0.060 0.100 5 0.020 0.030 0.050 (a) What is the probability that there is exactly one car and exactly one bus during a cycle? (b) What is the probability that there is at most one car and at most one bus during a cycle? (c) What is the probability that there is exactly one car during a cycle? Exactly one bus? P(exactly one car) = P(exactly one bus)- (d) Suppose the left-turn lane is to have a capacity of five cars and one bus is equivalent to three cars. What is the probability of an overflow during a cycle?

Explanation / Answer

a)

from the table,we check out the P(x,y) from second row and second column

we get probability =0.03

b)

Prob =0.01+0.015+0.02+0.03

               =0.075

c)

P(exactly one car) =0.02+0.03+0.05

                              =0.10

P(exactly one bus) =0.015+0.03+0.075+0.09+0.06+0.03

                                             =0.3

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