1) A student committee has 6 members -- 4 undergrad and 2 grad students. A subco
ID: 1179309 • Letter: 1
Question
1) A student committee has 6 members -- 4 undergrad and 2 grad students. A subcommittee of 3 members is to be chosen randomly so that each possible combination of 3 of the 6 students is equally likely to be selected. What is the probability that there will be no graduate students on the subcommittee?
2) A work crew for a building project is to be made up of 2 craftsmen and 4 laborers selected from a total of 5 craftsmen and 6 laborers.
a. How many different combinations are possible?
b. The brother of one of the craftsmen is a laborer. If the crew is selected at random, what is the probability that both brothers will be selected?
c. What is the probability that neither brother will be selected?
3) A campus student club distributed material about membership to new students attending an orientation meeting. Of those receiving this material 40% were men and 60% were women. Subsequently, it was found that 7% of the men and 9% of the women who received this material joined the club.
a. Find the probability that a randomly chosen new student who receives the membership material will join the club.
b. Find the probability that a randomly chosen new student who joins the club after receiving the membership material is a woman.
4) The grades of a freshman college class, obtained after the first year of college, were analyzed. Seventy percent of the students in the top quarter of the college class had graduated in the upper 10% of their high school class, as had 50% of the students in the middle half of the college class and 20% of the students in the bottom quarter of the college class.
a. What is the probability that a randomly chosen freshman graduated in the upper 10% of his high school class?
b. What is the probability that a randomly chosen freshman who graduated in the upper 10% of the high school class will be in the top quarter of the college class?
c. What is the probability that a randomly chosen freshman who did not graduate in the upper 10% of the high school class will not be in the top quarter of the college class?
Explanation / Answer
The possibility of the first undergraduate being chosen is 4/6 (4 undergraduates over the total committee)
Once that student has been removed, the possibility of the second undergraduate being chosen is 3/5 (3 remaining undergraduates over the remaining committee members)
After that, the possibility of the third undergraduate being chosen is 2/4 (last 2 undergraduates over the 4remaining students)
Multiply all the possibilities together
2/3 x 3/5 x 1/2 = 1/5
The probability of the subcommittee not having any graduate students is 1/5
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