Summary: ISyE 2027 Homework 1
Due January 23, Friday
1. A man receives presents from his three children, Allison, Betty and
Chelsea. To avoid disputes he opens the presents in a random order. What
are the possible outcomes?
2. Two boys are repeatedly playing a game that they each have probability
1/2 of winning. The first person to win five games wins the match. What
is the probability that Al will win if (a) he has won 4 games and Bobby has
won 3; (b) he leads by a score of 3 games to 2?
3. In a group of 320 high school graduates, only 160 went to college but 100
of the 170 men did. How many women did not go to college?
4. (a) How many license plates are possible if the first three places are
occupied by letters and the last three by numbers? (b) Assuming all com-
binations are equally likely, what is the probability the three letters and the
three numbers are different?
5. A basketball team has 5 players over six feet tall and 6 who are under
six feet. How many ways can they have their picture taken if the 5 taller
players stand in a row behind the 6 shorter players who are sitting on a row
6. A student studies 12 problems from which the professor will randomly