Algebra 2 Advanced
Ch.10 Probability Review
Name________________________
Period ___________
Please write your mathematical thinking clearly and circle your final answers.
1. A committee is to be formed consisting of 1 freshman, 1 sophomore, 2 juniors, and 2 seniors. How
many ways can this committee be formed from 5 freshmen, 5 sophomores, 8 juniors, and 10 seniors?
2. A local telephone number consists of 7 digits, and the first number cannot begin with 0 or 1. How
many different local telephone numbers are possible?
3. How many distinguishable ways can the letters in CASTRO be written?
4. How many distinguishable ways can the letters in MISSISSIPPI be written?
5. How many different 7 card hands are possible from a standard 52 card deck?
6. Solve for n.
a) n C7 = n C2
b) n P5  9( n P4 )
7. Find the binomial expansion of (2 x  3)5
8. Find the coefficient of x 4 in  3x 2  2 
5
9. 2 coins are tossed. What is the probability of getting at least one tail?
10. 4 coins are tossed. What is the probability of getting at least 3 tails?
11. Two dice are rolled. What is the probability of getting 7 or 11?
12. A lottery is played with 52 numbers, and a winner must choose all 6 winning numbers. What is
the probability of winning this lottery?
13. From a standard deck of 52 cards, find the probability of getting a club, or a face card.
14. John moves to Thailand, and only speaks English. On his first day of school he is given a 10
question multiple choice quiz in Thai, each with 4 options. What is the probability that John will
guess all 10 questions correctly?
15. A bag contains 3 blue, 4 purple, and 5 red marbles. 3 marbles are drawn. Find the probability of
drawing:
a) 3 purple
b) one of each color
c) 2 red and a blue
d) 2 blue and an orange
e) a blue, given you drew 2 reds
16. A dice is rolled. Find the probability of rolling a number that is less than 5, or even.
17. A spinner is divided into 15 equal regions numbered 1 to 15. What is the probability that 4
consecutive spins result in prime numbers?
18. You randomly select 2 cards from a standard deck of 52 cards.
What is the probability that the first card is a heart and the second card is a club if
(a) you replace the first card before selecting the second, and
(b) you do not replace the first card?
19. How many different 7-digit telephone numbers are possible if the first digit is not 0 or 9 and the
last digit is 4 or 5?
20. A store sells T-shirts in 5 colors, 9 designs, and 3 sizes. How many different T-shirts are
available?
21. Ten runners are in a cross-country race. How many different possibilities are there for listing first,
second, and third place finishers?
22. The odds of an event occurring are 15 to 7. What is the probability of the event occurring?
23.
How many 5 member basketball teams can be formed from 11 people?
24. A coin purse contains 4 pennies, 5 nickels, and 8 dimes. Four coins are selected randomly. Find
the probability that there are 2 pennies and 2 dimes.
25. Three cards are drawn from a standard deck of 52 cards. Find the probability that all three cards
are spades.
26. An urn holds 6 red marbles, 9 white marbles, and 4 blue marbles. 3 marbles are randomly
selected from the urn. Find the probability that the first is red, the second is white, and the third is blue,
in that order.
27. Two cards are drawn from a standard deck of 52 cards. Find the probability that the two cards
are both queens or both are black cards.
28. From a group of 8 men and 6 women, a committee of 3 is to be selected at random. Find the
probability that the committee has 3 men or 3 women.
29. Suppose the probability of rain in a certain city is 1/3 on any given day. What is the probability
that rain will fall on at least one day of a three-day visit to the city?
30. A high school basketball team leads at halftime in 45% of the games in a season. The team wins
75% of the time when they have a halftime lead, but wins only 9% of the time when they do not have a
halftime lead. What is the probability that the team wins a particular game during the season?
Answer
1) 31,500 2) 8,000,000 3) 720 4) 34,650 5) 133,784,560 6) a. 9, b. 13
7) 32 x5  240 x 4  720 x3  1080 x 2  810 x  243 8) -720 9) ¾ 10) 5/16 11) 2/9 12) 4.9 108
1
13) 11/26 14) ( )10 or 9.5 10 7 15) a. 1/55 b. 3/11 c. 3/22 d. 0 e. 3/10 16) 5/6 17) 0.0256
4
18) a. 0.0625 b. 0.0637 19) 1, 600, 000 20) 135 21) 720 22) 15/22 23) 462 24) 0.0706
25) 0.0129 26) 0.0372 27) 0.249 28) 0.209 29) 0.704 30) 0.387