2. Four students attempt to register online at the same time for an Introductory

Question

2. Four students attempt to register online at the same time for an Introductory Statistics class that is full. Two are freshmen and two are sophomores. They are put on a wait list. Prior to the start of the semester, two enrolled students drop the course, so the professor decides to randomly select two of the four wait list students and gives them a seat in the class.
What is the probability that both students selected are freshmen?

5. A club is choosing 2 members to serve on a committee. The club has nominated 1 women and 3 men. Based on chance alone, what is the probability that one woman and one man will be chosen to be on the committee?

6. A club is choosing 2 members to serve on a committee. The club has nominated 4 women and 2 men. Based on chance alone, what is the probability no women are chosen to be on the committee?

7. An urn contains 24 red marbles, 21 blue marbles, and 41 yellow marbles. One marble is to be chosen from the urn without looking. What is the probability of choosing a red marble?

8. An urn contains 16 red marbles, 25 blue marbles, and 44 yellow marbles. One marble is to be chosen from the urn without looking. What is the probability of choosing a red or a blue marble?

Explanation / Answer

#2.
2 students from 4 wait listed can be selected in 4C2 ways
2 freshmen can be selected in 1 way
Required probability = 1/4C2 = 0.1667

#5.
2 persons from 4 can be selected in 4C2 ways
Required probability = 1*2C1/4C2 = 2/6 = 1/3 = 0.3333

#6.
From 6, two can be selected in 6C2 ways
Required probability = 2C2/6C2 = 1/15 = 0.0667

#7.
total 24+21+44 = 89 marbles, 1 can be selected in 89C1 ways
Required probability = 24C1/89C1 = 24/89 = 0.2697

#8.
Total 16+25+44 = 85 marbles, 1 can be selected in 85C1 ways
Required probability = (16C1 + 25C1)/85C1 = 41/85 = 0.4824

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