Question 52671: A small town has 5,600 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 sex.
Men Women Total
In Favor 1,400 280 1,680
Opposed 840 3,080 3,920
Total 2,240 3,360 5,600
Let: M be the event a resident is a man
W be the event a resident is a woman
F be the event a resident is in favor
P be the event a resident is opposed
a. Find the joint probability table.
b. Find the marginal probabilities.
c. What is the probability that a randomly selected resident is a man and is in favor of building the bridge?
d. What is the probability that a randomly selected resident is a man?
e. What is the probability that a randomly selected resident is in favor of building the bridge?
f. What is the probability that a randomly selected resident is a man or in favor of building the bridge?
g. A randomly selected resident turns out to be male. Compute the probability that he is in favor of building the bridge.
Answer by stanbon(75887)   (Show Source):
You can put this solution on YOUR website! Men Women Total
In Favor 1,400 280 1,680
Opposed 840 3,080 3,920
Total 2,240 3,360 5,600
Let: M be the event a resident is a man
W be the event a resident is a woman
F be the event a resident is in favor
P be the event a resident is opposed
a. Find the joint probability table.
Need figure prob of M&F, W&F, M&O, W&O
For example P(M&F)=1400/5600=0.25
b. Find the marginal probabilities.
Nee figure Prob of M, of W, of F, or O
For example P(M)=3920/5600=0.70
c. What is the probability that a randomly selected resident is a man and is in favor of building the bridge?
Prob(M&F)= 0.25 as we figured above
d. What is the probability that a randomly selected resident is a man?
P(M)=3920/5600=0.70
e. What is the probability that a randomly selected resident is in favor of building the bridge?
P(F)=1680/5600=0.30
f. What is the probability that a randomly selected resident is a man or in favor of building the bridge?
P(M or F)= P(M)+P(F)-P(M&f)= [3920+1680-1400]/5600=4200/5600=0.75
g. A randomly selected resident turns out to be male. Compute the probability that he is in favor of building the bridge.
P(F|M)= 1400/2240=0.625
Cheers,
Stan H.
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