1. A company has decided to hire 3 new employees. There are 25 people who apply
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Question
1. A company has decided to hire 3 new employees. There are 25 people who apply for the job. How many different ways could 3 people be chosen from the 25 applicants?
2. We are interested in looking at probabilities related to the weather in Chicago in January of 2016. During this month, there were 16 days that had a high temperature above freezing, 12 days it either snowed or rained, and 7 days it was both above freezing and rained or snowed.
a. What percentage of days did it neither snow/rain NOR hit above freezing?
b. Are H and D mutually exclusive events? Why or why not?
c. Are the two events, H and D, independent? Explain, using probabilities.
d. If we know that it hit above freezing, what is the probability it also rained or snowed?
Explanation / Answer
1) Number of ways to choose 3 people from 25 applicants = 25C3 = 25! / (22! * 3!)
= 2300
2) Let H be the event of high temperature above freezing
and D be teh event of snowed or rained.
P(H) = 16/30 = 0.5333
P(D) = 12/30 = 0.4
P(H and D) = 7/30 = 0.2333
P(H or D) = P(H) + P(D) - P(H and D)
= 0.533 + 0.4 - 0.233
= 0.7
a)percentage of days did it neither snow/rain NOR hit above freezing = 1 - P(H or D)
= 1 - 0.7
=0.3
= 30%
b)
No, H and D are not mutually exclusive events. Because Both the events can happen at same time.
c) P(H) * P(D) = 16 * 12 / (30 * 30) = 0.2133
Since, P(H) * P(D) not equals to P(H and D), They are not independent events.
d) P(D | H) = P(H and D) / P(H)
= (7/30) / (16/30)
= 7 / 16
= 0.4375
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