Nov. 14, 2000
(1) Suppose a college has 1200 students, 600 of whom are men. Suppose also that 500 students are democrats, and that 200 students are women who are not democrats.
(a) How many students in the college are women?
(b) How many of these women are democrats?
(c) How many men are democrats?
(d) How many men are not democrats?
(a) A pizza resturant offers 10 pizza toppings. Their weekly special is a pizza
with any 3 toppings for $8.
How many different combinations of 3 toppings could be ordered?
(b) Meanwhile, in the kitchen, the cook has 10 boxes of toppings, and is lining
them up on his shelf.
In how many ways can he do this?
(3) In a certain lottery, a bin contains 10 balls, each labled with a different number between 1 and 10. Six of these balls will be drawn out and lined up in a sequence. You buy a ticket, and write a sequence of six different numbers between 1 and 10 on it. You win $10,000 if the sequence of numbers on your ticket matches the sequence of numbers that is drawn (i.e. in the same order). What are your chances of winning?
(4) One card is drawn off a 52-card deck. What is the probability that
(a) black or a Jack?
(b) a club but not a Jack?
(c) neither black nor a Jack?
(d) black, given that it's a Jack?
(5) A die is rolled 6 times. What is the probability that ...
(a) the first 2 rolls are ones?
(b) exactly 2 of the 6 rolls are ones?
(c) the same number is rolled each time?
(d) the first roll is a one or the last roll is a six?
(6) At a certain college, 30% of the students are freshmen. Also, 80% of the freshmen live on campus, while only 60% of the remaining students live on campus.
(a) A student is chosen at random. What is the probability that the student is a freshman who lives off campus?
(b) A student is chosen at random. If the student lives on campus, what is the probability that the student is a freshman?
(7) A box contains 2 red balls, 3 blue balls, and 1 green ball. You draw two balls, one after the other (without replacement). What is the probability that...
(a) both draws are red?
(b) both draws are blue?
(c) the same color is drawn both times?