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Scholarship Precalculus
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Probability Review
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For each of the following, label and shade the region of the Venn diagram described by the set.
1. A  B
2. A ' B '
3. A   B  C  '
For questions 4 & 5, use the Venn diagram to illustrate the situation by labeling and determining the
numbers for each section. Then use the diagram to answer the question asked.
4. Of the 52 teachers at Roosevelt High School, 27 said they like to run for exercise, 25 said they like to
go biking, and 12 said they don’t enjoy either activity. How many enjoy biking but not running?
5. Of the 50 girls in a 6th grade class, 23 have blue eyes, 21 have curly hair, and 22 have brown hair. 10
girls have all three characteristics, while 6 have blue eyes (but not brown or curly hair), 5 have curly
hair (but not blue eyes or brown hair), and 7 have brown hair (but not blue eyes or curly hair). How
many girls have none of the three characteristics mentioned?
6. How many odd positive integers less than 1000 can be written using the digits 0, 3, 6, 7, 8, and 9?
7. In how many ways can 4 of 7 different kinds of bushes be planted along one side of a house?
8. How many distinguishable ways can the letters of the word BEEKEEPER be arranged? Show how to
simplify the expression.
9. Solve for n: n P5
14 n P4
10. In a group of 10 people, each person shakes hands with everyone else once. How many handshakes
are there?
11. The junior and senior class councils each have 10 members. In how many ways can a prom
committee be formed if it must consist of 3 seniors and 2 juniors?
12. How many diagonals does a regular tetracontagon (40-sided polygon) have?
13. Find the 11th term in the expansion of a 2b
14
.
14. Find the coefficient of the a2b9 term in the expansion of 5a
5
3b3 .
15. A bag contains 3 red, 2 blue, 1 orange, and 4 green marbles. Two marbles are drawn from the bag
(without replacement).
a) What is the sample space of the experiment?
b) What is the probability of drawing a blue marble and then a green marble?
16. Two standard dice (numbered 1-6) are rolled. Find the probability of each event.
a) The sum of the numbers is less than 5.
b) The sum of the numbers is 4 or 5.
c) The sum is at least 7.
17. There are 12 tulip bulbs in a package. Nine will yield yellow tulips and three will yield red tulips. If
two tulip bulbs are selected at random find the probability of each event.
a) Both tulips will be red.
b) One tulip will be yellow and the other red.
18. The probability of rain on a certain day is 65% in Yellow Falls and 40% in Copper Creek. Find the
probability of each event.
a) It will rain in Yellow Falls but not in Copper Creek.
c) It will rain in neither town.
b) It will rain in both towns.
d) It will rain in at least one of the towns.
19. A committee of 5 people is to be formed from a group of 7 men and 6 women.
a) How many different committees can be formed?
b) Write the probability in terms of combinations of the committee having 3 men and 2 women.
c) Write the probability in terms of combinations of the committee having at least 3 women.
20. A hand of 7 cards is dealt from a well-shuffled standard deck.
a) How many different hands contain exactly 3 spades?
b) What is the probability of getting all hearts? Write in terms of combinations.
c) What is the probability of getting 2 kings and 2 queens? Write in terms of combinations.
d) What is probability of getting one heart, one diamond, one spade, and the rest clubs? Write in
terms of combinations.