Question

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 a Woman?

B) What is the probability that a randomly selected resident is a Woman and is in Favor of the bridge?

C) What is the probability of a randomly selected resident being a Woman or in Favor of 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" with probabilities.

2. How many Combinations of 4 students can be selected from a group of 9 students?

3. Describe the Sample Space for the experiment of selecting one card from a deck of regular playing cards?

Answer 1

A) Total number of women = 3360

     Total number of residents = 5600

Probability of a randomly selected resident being a Woman

= Total number of women / Total number of residents

= 3360 / 5600

= 0.6

Probability of a randomly selected resident being a Woman is 0.6

B)

Number of women who are in favor of the bridge = 280

Total number of residents = 5600

Total number of women = 3360

Probability that a randomly selected resident is a Woman and is in Favor of the bridge

= P(resident is a Woman) * P(resident is in favor of the bridge)

= (Total number of women / Total number of residents) * (Number of resident who are in favor of the bridge / Total number of residents)

= (3360/5600) * (1680/5600)

= 0.6 * 0.3

= 0.18

Probability that a randomly selected resident is a Woman and is in Favor of the bridge is 0.18

C)

Number of women who are in favor of the bridge = 280

Total number of residents = 5600

Total number of women = 3360

Probability of a randomly selected resident being a Woman or in Favor of the bridge

= P(resident is a Woman) + P(residents in favor of the bridge) - P( women who are in favor of the bridge)

= (3360/5600) + (1680/5600) - (280/5600)

= 0.6+ 0.3 - 0.05

= 0.85

Probability of a randomly selected resident being a Woman or in Favor of the bridge is 0.85

D)

Total number of men = 2240

     Total number of residents = 5600

Probability of a randomly selected resident being a man

= Total number of men / Total number of residents

= 2240 / 5600

= 0.4

Probability of a randomly selected resident being a man is 0.4