1 A small town has 5600 residents The residents in the town

1. A small town has 5600 residents. The residents in the town were asked whether or not they favored building a new bridge across the river. You are given the following information on the residents\' responses, broken down by gender:

                                        Men          Women          Total

          In Favor                  1400            280               1680

          Opposed                  840           3080               3920

                Total                2240           3360               5600

A) What is the probability of a randomly selected resident being in opposed to the bridge?

B) What is the probability that a randomly selected resident is a man and is Opposed to the bridge?

C) What is the probability of a randomly selected resident being a man or Opposed to the bridge?

D) If a randomly selected resident is a man, what is the probability that he is in favor of the bridge?

E) Are gender and opinion about the bridge mutually exclusive events? Why?

F) Are gender and opinion about the bridge independent events? Why? Show some \"proof\".

Solution

a)

P(opposed) = (840+3080)/5600 = 0.7 [answer]

b)

P(man and opposed) = 840/5600 = 0.15 [answer]

c)

P(man OR opposed) = (1400 + 840 + 3080)/5600 = 0.95 [answer]

d)

P(favor|man) = 1400 / 2240 = 0.625 [answer]

e)

No. As we can see, P(man and opposed) = 0.15, which is not 0. Thus, they have intersections, so, they are NOT MUTUALLY EXCLUSIVE.

f)

As P(favor|man) = 0.625, P(favor) = 1680/5600 = 0.3, we see that they are not independent, as P(favor|man) =/= P(favor).