1. A pair of dice are rolled. Find the probability of rolling a 7 or a 5.
2. Two students are selected at random from a class of ten males and seven females. Find the probability
that both students are males.
3. A card is drawn from a deck of poker cards. Find the probability that it is
a) a three
b) a 10 or a jack
c) not a diamond
4. Pablo wrote 18 thank-you notes and had stamps for 10 of them. If one of the notes is selected at
random, find the probability that it will be
a) a stamped note
b) a note that is not stamped
c) a note that is stamped or one that is not stamped
5. A tray of electronic components contains 15 components, four of which are defective. If four
components are selected, what is the probability that
a) all four are defective?
b) three are defective and one is good?
c) exactly two are defective?
d) none are defective?
e) at least one component is good?
6. A club has ten members and six pledges. Five of them are arranged in sequence for a club meeting.
The five are selected and seated at random.
a) Find the probability that members are in seats 1 and 2 and pledges are in seats 3 through 5.
b) Find the probability that members and pledges alternate seats with members in seats 1, 3, 5 and
pledges in seats 2 and 4.
7. There are 12 freshmen and 9 sophomores in a class. If three students are selected at random, find the
probability that two are freshmen and one is a sophomore.
8. A child has eight cans of soft drinks, four different brands with one regular and one diet drink for each
brand. The child arranges four of the cans in a row in a random manner.
a) Find the probability that the arrangement consists of all diet drinks.
b) Find the probability that the first two are diet drinks and the second two are regular.
9. The probability that the university football team will win is 0.6, and the probability that it will loose is
0.3. What is the probability of a tie?
10. A child has nine cards numbered 1 through 9. The child places three cards in a row to form a threedigit number. Find the probability that the number is larger than 500.
11. An urn contains six blue balls, five yellow balls, and three white balls. If a ball is drawn at random,
find the probability that
a) it is yellow
b) it is not yellow
12. Fifteen cards are numbered 1 through 15. The cards are shuffled, and three cards are drawn and
arranged in a row.
a) Find the probability that all three are odd.
b) Find the probability that the first two are odd and the third is even.
c) Find the probability that the arrangement consists of three cards larger than 10.
13. A shipment of 14 televisions contains six regular and eight deluxe models. The manufacturer failed to
mark the model designation on the cartons. If four cartons are selected at random, what is the
probability that exactly three of them are the deluxe model?
14. A mathematics class is composed of 12 freshmen, 10 sophomores, and 6 juniors. Three of the
freshmen, two of the sophomores, and one junior receive ‘A’ grades in the course. If a student is
selected at random from the class, find the probability that
a) the student is an ‘A’ student
b) the student is an ‘A’ freshman student
c) the student is a sophomore or an ‘A’ student
15. Linda types a letter and envelope addressed to each of five people. A temporary worker inserts a
letter in each envelope without looking.
a) Find the probability that all letters are placed in the correct envelopes.
b) If two letters are addressed out of state and three are addressed in state, find the probability
that the in-state letters are put into in-state envelopes and the out-of-state letters are put into
out-of-state envelopes.
16. In the game of Greed a player rolls six dice. If all the numbers 1 through 6 turn up, the player
receives 1500 points. Find the probability that this occurs.
17. The New York lottery draws six numbers out of 40, and the order doesn’t matter.
a) How many ways can this be done?
b) A player chooses six numbers. What is the probability that the player wins the lottery?
18. A car has six spark plugs, two of which are malfunctioning. If two of the plugs are replaced at
random, what is the probability that both malfunctioning plugs are replaced?
19. A box contains five yellow balls, three green balls, and two red balls. A sequence of three different
balls is drawn.
a) Find the probability a green, a yellow, and a red ball are drawn in that order.
b) Find the probability the first two are yellow and the third is red.
c) Find the probability that a green, then a red, then a green are drawn.
20. A student is to be selected from a group of six students. For each classification of freshman and
sophomore there is a math major, an art major, and a biology major. The probability of each
individual being selected is given in the following table:
Freshman
Sophomore
Math
0.10
0.22
Art
0.08
0.30
Biology
0.17
0.13
Find the probability that
a) the individual selected is a freshman or an art major is chosen.
b) the individual selected is a freshman math major or a sophomore is chosen.
c) the individual selected is a math or art major and a sophomore.