5.B A certain stretch of highway on the New Jersey Turnpike has a posted speed l

Question

5.B A certain stretch of highway on the New Jersey Turnpike has a posted speed limit of 60

mph. A survey of drivers on this portion of the turnpike revealed the following facts:

18% of the drivers were female

89% of the drivers were exceeding the speed limit by at least 5 mph (and subject to being stopped)

Of those speeding, 15% of the drivers were female

(a) Using F for female and S for speeding, convert each of the bullets above into probability

statements.

(b) Find the probability that a driver on this stretch of highway is female and exceeding the speed limit.

(c) Given a driver on this stretch of highway is female, what is the probability that the driver is speeding?

(d) Given that a driver on this stretch of highway speeding, what is the probability that the driver is male?

(e) For this stretch of highway, are being female and exceeding the speed limit independent or dependent events? Explain using probabilities.

(f) For this stretch of highway, are being female and exceeding the speed limit mutually exclusive (disjoint) events? Explain using probabilities.

Explanation / Answer

a)

P(F) = 0.18
P(S) = 0.89
P(F|S) = 0.15 [ANSWERS]

b)

P(F n S) = P(F|S) P(S) = 0.15*0.89 = 0.1335 [ANSWER]

**************

C)

P(S|F) = P(F n S)/P(F) = 0.1335/0.18 = 0.741666667 [ANSWER]

**************

d)

P(M|S) = 1 - P(F|S) = 1 - 0.15 = 0.85 [ANSWER]

******************

e)

As

P(F|S) = 0.15 =/= P(F), then NO, THEY ARE NOT INDEPENDENT.

*****************

f)

As

P(F n S) =/= 0, then NO, THEY ARE NOT MUTUALLY EXCLUSIVE.

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