A recent survey on Canadian Firearms Regulations suggested that 71.4% of Canadia
ID: 3305206 • Letter: A
Question
A recent survey on Canadian Firearms Regulations suggested that 71.4% of Canadians supported stronger gun laws, while 28.6% believe that current gun laws are strong enough and do not need strengthening.
In addition, 54.58% of males support stronger gun laws in Canada while 87.62% of females support stronger gun laws. Assume 50.9% of Canadians are female.
a) Find the probability this person is female and supports stronger gun laws.
b) Suppose the person chosen does not support stronger gun laws. Find the probability this person is female.
c) If the randomly chosen person does support stronger gun laws, what is the probability this person is male?
Explanation / Answer
a) Probability that the person is female P(A) = 50.9% = 0.509
Probability that she supports stronger gun laws P(B) = 0.862
=> Probability that the person is female and she supports stronger gun laws P(A B)
= 0.509 * 0.862
= 0.4388
b) Probability that a person is female P(A) = 0.509
Probability that she does not support stronger gun laws P(A Bc) = P(A) - P(A B)
= 0.509 - 0.4388 = 0.0702
=> Probability that a person is female given she does not support gun laws P(A|Bc) = P(A Bc) / P(Bc)
= 0.0702 / 0.286
= 0.245
c) Probability that a person is male given he does support stronger gun laws
P(Ac|B) = 1 - P(A|B)
= 1 - P(A B) / P(B)
= 1 - 0.4388 / 0.862
= 0.49