Texas A&M University
Department of Mathematics
Volodymyr Nekrashevych
Fall 2011
Math 411 — Problem Set 2
Issued: 09.09
Due: 09.16
2.1. A bet is said to carry 3 to 1 odds if you win $3 for each $1 you bet.
What must the probability of winning be for this to be a fair bet?
2.2. Five people play a game of “odd man out” to determine who will
pay for the pizza they ordered. Each flips a coin. If only one person
gets heads (or tails) while the other four get tails (or heads) then he is
the odd man and has to pay. Otherwise they flip again. What is the
expected number of tosses needed to determine who will pay?
2.3. A man and his wife decide that they will keep having children until
they have one of each sex. Ignoring the possibility of twins and supposing that each trial is independent and results in a boy or a girl with
probability 1/2, what is the expected value of the number of children
they will have?
2.4. Suppose we pick a month at random from a non-leap year calendar
and let X be the number of days in the month. Find the mean and
variance of X.
2.5. Can we have a random variable with EX = 3 and EX 2 = 8?
2.6. In a class of 19 students, 7 will get A’s. In how many ways can this
set of students be chosen?