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Math 7/8 Unit 1 Probability & Set Theory Review
Name ______________________
1) Is it possible to have a probability greater than 100%? Explain.
2) How do you calculate the outcomes of the following:
A) P(A or B)?
B) P(A and B)?
3) Shade in the sets:
A  B  C
AB
4) Draw a tree diagram of all the possible outcomes of tossing a coin and rolling a 10-sided number cube.
How many possible outcomes are there?____What is P( heads, prime number)?____
5) A box contains 8 green marbles, 7 purple marbles, and 14 orange marbles.
What is the P(green, then orange) if a marble is selected and replaced, and then a second marble is
selected?
6) Find the number of possible outcomes if you had a choice of 3 different cars, 6 different models and 12
different color choices.
7) The universal set includes the letters of the alphabet. Set A={vowels}. What is A’?
8) License plates in a certain state contain 4 letters followed by 5 digits. Assume that all combinations are
equally likely. Show how you would calculate the number of possible license plates.
9) Florida has 23 members in the United States House of Representatives. Ten members are Democrats,
13 are Republicans and of those, 18 are men. The Speaker of the House wants to choose a
representative from Florida at random to serve on the agriculture committee.
What is P(man or republican)?
10) If 2/3 of all households have some kind of pet, and 1/5 of all households have at least one child. If a
household is picked at random, what is P(pet and one or more children)?
11) What is A B if A = {f, a, c, t, o, r} and B = {m, u, l, t, i, p, l, e}?
12) Lynnwood High School requires all staff members to have a 5-character computer password that
contains 3 letters followed by 2 numbers. Find the number of possible passwords.
13) If A and B are independent events such that P(A)=
1
2
and P(B)= , what is P(A and B)?
6
9
14) If set A = {1, 2, 3, 4, 5, 6} and B = {1, 3, 5, 7, 9, 11}, what is A B?
15) The lottery has 10 balls in each machine containing numbers 0-9. There are 4 different machines. What
is the probability that each machine would produce a 5?
16) Sarah rolls two 6-sided numbered cubes. What is the probability that the two numbers added together
will equal 3?
17) The eighth grade graduation party is being catered. The caterers offer 3 appetizers, 4 salads, and 3
main courses for each eighth grade student to choose for dinner. If the caterers would like 72 different
combinations of dinners, how many desserts should they offer?
18) There are 52 cards in a deck. What is the probability of drawing a king or a spade? Hint: There are 4
different suits with 13 cards each: 2-10, jack, queen, king, ace.
19) There are 52 cards in a deck. What is the probability of drawing a queen, replacing it, and then drawing
a jack? Hint: There are 4 different suits with 13 cards each: 2-10, jack, queen, king, ace.
20) If A and B are independent events such that P(A)=0.6 and P(B)=0.36, what is the P(A or B)?
Write the symbol:
union _______
intersection _________
complement __________
subset ______
not a subset ________
element __________
null set _____
not an element _____
set ______