8. (5 points) The probability that traffic will be banned around the town square

Question

8. (5 points) The probability that traffic will be banned around the town square if certain legislation is passed is 0.85. The probability that traffic will be banned if the legislation in question does not pass is 0.20. The likelihood that the legislation will pass is 40%. a. Make a probability tree to illustrate this problem b. If the probability that the legislation will pass is 0.40, what is the probability that the traffic will not be banned? c. if we just learned that the traffic around town square was banned, what is the probability that the legislation did not pass?

Explanation / Answer

P(legislation will pass) = 0.4

P(legislation will not pass) = 1 - P(legislation will pass) = 1 - 0.4 = 0.6

P(Traffic will be banned | legislation is passed) = 0.85

P(Traffic will be banned | legislation is not passed) = 0.20

b) P(Traffic will be banned) = P(Traffic will be banned | legislation is passed) * P(legislation is passed) + P(Traffic will be banned | legislation is not passed) * P(legislation is not passed)

                                           = 0.85 * 0.4 + 0.2 * 0.6

                                           = 0.46

P(Traffic will not be banned) = 1 - P(Traffic will be banned)

                                             = 1 - 0.46

                                             = 0.54

c) P(legislation dis not pass | Traffic will be banned) = P(Traffic will be banned | legislation is not passed) * P(legislation is not passed) / P(legislation is not passed)

                                                                                = 0.2 * 0.6 / 0.54

                                                                                = 0.22

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