1. Two people are to be selected from a group of five employees: Jane, Jan, Jack
ID: 2930786 • Letter: 1
Question
1. Two people are to be selected from a group of five employees: Jane, Jan, Jack, John and Joe.
a. How many ways are there to create a committee of two people, assuming order does not matter?
b. If each committee (again, order does not matter) is equally likely to be created, what is the probability that Jack will be on the committee?
c. Jan and Jane have special certifications that the others don’t. What is the probability that at least Jan or Jane will be selected to the committee?
d. If order did matter (say the first person selected is the chair of the committee and the second selected is the assistant), how many ways are there to create a committee of 2 members?
Explanation / Answer
a. There are 5 people and we need to choose 2. This can be done in 5C2 = 10 ways.
b. Since Jack will be on the committee, we have 4 choices for the other person.
=> Number of committees formed with Jack in it = 4.
=> Probability that Jack is in a committee = 4/10 = 0.4.
c. Probability that Jan is in the committee = 0.4
Probability that Jane is in the comittee = 0.4
Probability that Jan and Jane are both in the committee = 1/10 = 0.1
=> Probability that atleast Jan or Jane are in the committee = 0.4 + 0.4 - 0.1 = 0.7.
d. Since there are 5 people and 2 need to be arranged, we can do this in 5P2 ways
= 20 ways.
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