Question

1. We roll two fair 6-sided dice. Compute the probabilities of the following events.

(a) The sum is at most 6.

(b) The sum is more than 6.

(c) The sum is at most 6 and at least one die is a 4.

2. Consider the letters a,b,c. Suppose we draw 2 of the letters at random (allowing for repetition). Assume order matters. That is, ab is not the same as ba:

Let A : The 2 letters are distinct.

B : At least one letter is a

C : The first letter is a

(a) List the members of the sample space S and the events A, B, and C

(b) Are A and B independent? Are A and C independent?

(d) The sum is at most 6 given that at least one die is a 4.

(e) The sum is at most 6 given exactly 1 die is a 4

3. A bag contains 24 red marbles and 6 blue marbles. We select 4 marbles from the bag at random.

(a) What is the probability at least one of the marbles is blue?

(b) What is the probability at most one of the selected marbles is blue?

4. Two cards are drawn at random from a 52 card deck.

(a) How many two-card combinations are possible?

(b) What is the probability the 2 cards are not a pair?

(c) What is the probability exactly one card is an ace.

(d) What is the probability at least one the cards is an ace?

5. A batch of 48 parts contains 8 defective parts. You select 20 parts at random from this batch.

(a) How many defective parts would you expect to nd (on average) in the sample of 20?

(b) What is the probability of finding at least two defective parts in the sample?

Answer 1