# Math 411 — Problem Set 1 Issued: 09.02 Due: 09.09

```Texas A&amp;M University
Department of Mathematics
Volodymyr Nekrashevych
Fall 2011
Math 411 — Problem Set 1
Issued: 09.02
Due: 09.09
1.1. Two dice are rolled. What is the probability that (a) the two numbers
will differ by 1 or less and (b) the maximum of the two numbers will
be 5 or larger?
1.2. Suppose Ω = {a, b, c}, P ({a, b}) = 0.7, and P ({b, c}) = 0.6. Compute
the probabilities of {a}, {b}, and {c}.
1.3. Given two events A and B with P (A) = 0.4, and P (B) = 0.7, what
are the maximum and minimum possible values for P (A ∩ B)?
1.4. A family has 3 children, each of whom is a boy or a girl with probability
1/2. Let A = “there is at most 1 girl” B = “the family has children
of both sexes.” (a) Are A and B independent? (b) Are A and B
independent if the family has 4 children?
1.5. Roll two dice. Let A = “the sum is even” and B = “the sum is divisible
by 3,” that is B ∈ {3, 6, 9, 12}. Are A and B independent?
1.6. Suppose we roll three tetrahedral dice that have 1, 2, 3, and 4 on their
four sides. Find the distribution of the sum of the three numbers.
```