a) Assuming that the traits of red hair and blond hair are mutually exclusive, Rule 2 can be applied. so the probability is 23% - 14% = 9%
b) 0.247
c) 0.9761
Problem 3.
a) This contradicts rule 1
b) A probability cannot exceed 1
c) This contradicts Rule 4. Red sports cars are a subset of red cars so the probability that a car is red cannot be less than the probability that it is both red and a sports car.
Problem 10.
No to say that the probability is 5/10, you are assuming that the events are mutually exclusive, but you could easily get an interesting piece of mail on two of these days or all of them.
Problem 11.
We would have to assume independence, so that if a person belongs to one of these organizations, it would not make them more or less likely to belong to the other. This assumption is probably not valid because older people are more likely to belong to AAA, and only those over 50 are allowed to belong to AARP.
Problem 12.
By Rule 4, alternative A must have a higher probability than B, because feminist bank tellers are a subset of bank tellers.
Problem 15.
a) 11/12
b) 10/12
c) 11*10/(12*12)
d) 34/144
Problem 17.
a) likely not independent
b) not independent
c) independent
d) likely independent
Problem 19.
a) 99/100
b) .0099
Problem 20.
a) (684,999/685,000)^70
b) 1 minus the answer in a.
c) These probabilities do not apply to any particular person. Your chances depend on things like where you live and what you do during storms.
d) approximately 380 people.
Problem 21.
a) the expected commute time is 16 minutes.
b) No the commute times are always either 15 or 20 min, this is just an average over the long run.
Problem 27.
the probability that results in a break even situation is cost/(cost + 5000).