1. Determine the sample space for the following experiments.
(a) A student is selected at random and his GPA is recorded.
(b) A player chooses two cards at random from a standard deck of cards and records
their sum. (Assume face cards have a value of 10 and aces can take a value of 1
or 11, as in black jack.)
(c) Choose an odd number from 1 to 13 at random.
2. A jar contains 3 red, 2 green, 4 blue, and 3 yellow marbles. If a single marble is chosen at random from the jar and its color recorded, give the sample space. What is the probability of each possible outcome?
3. A three-die is a six-sided die with two sides labeled 1, two sides labeled 2, and two
sides labeled 3. Two three-dice are rolled and the numbers face up on the two dice are
recorded. Give the sample space for this experiment. What is the probability that at
least one of the dice rolled is showing a 2?
4. Two three-dice are rolled and their sum is recorded. (a) Give the sample space for this
experiment. (b) What is the probability of rolling a sum of 4? (Hint: Your work in #
3 might be helpful.) (c) Give the probability of each of the outcomes in your sample
space. Show that P(S) = 1 where S is the sample space.
5. Seven six-sided dice are rolled. Find the following probabilities.
(a) The probability that at least one of the dice rolled is showing a six.
(b) The probability that the sum of the dice is greater than 8.
6. A box contains 40 blocks. For each of the colors red, blue, green, or yellow there are
10 blocks of the color labeled with a number 1-10. You reach into the box and draw a
block. Let E be the event that the block drawn is red and let F be the event that the
block drawn is labeled with an even number.
(a) Describe the event E in words.
(b) Describe the event E ∩ F in words.
(c) Find the following probabilities.
i. P(E) ii. P(F) iii. P(E ∩ F)
iv. P(E ∪ F) v. P(E) vi. P(E ∩ F) vii. P(E ∪ F)
7. Three students from a 15 student class will be selected to attend a meeting. Six of the
students are female.
(a) What is the probability that all three of the students chosen to attend the meeting
are female?
(b) What is the probability that not all three of the students chosen to attend the
meeting are female?
8. If we draw a five card hand from a standard 52 card deck, what is the probability that
all five cards are hearts?
9. In the game of euchre, the deck consists of the 9, 10, jack, queen, king and ace of each suit. Players are dealt a five card hand.
(a) What is the probability that a player is dealt five hearts?
(b) What is the probability that a player is dealt two red jacks?
