Name____________________________________
Probability Review
Date______
10H Per___
1. Tanika is trying to decide on her class schedule for her senior year in high school. She has a list of 10 classes she would like
to take, but room to only take 6 of these classes.
a) How many different selections of 6 classes can Tanika make from her 10 choices?
b) How many different schedules could Tanika have? Assume that none of the classes conflict with one another and that
taking a classes a different period constitutes a different schedule.
2. How many three-letter codes can be made out of the letters in the word BASIC?
(a) 60
(b) 5
(c) 10
(d) 36
3. How many distinct arrangements of letters can be formed from the word ONOMATOPOEIA?
4. Jim can drive a golf ball over 220 yards 40% of the time. He regularly plays on a golf course where drives of that distance
are needed on 12 holes. Determine the probability that exactly 7 of his drives will be over 220 yards.
5. The probability of rain on the last day of July is 90%. If the probability remains constant for the first seven days of August,
what is the probability that it will rain at least six of those seven days in August?
6. According to a federal agency, when a lie detector test is given to a truthful person, the probability that the test will show
that the person is not telling the truth is 20%. If a company interviews five truthful candidates for a job and asks about
thefts from prior employers, what is the probability a lie detector test will show that at most one candidate is not telling the
truth?
7. The accompanying diagram shows a square dartboard. The side of the dartboard measures 30 inches. The square shaded
region at the center has a side that measures 10 inches. If darts thrown at the board are equally likely to land anywhere on
the board, what is the theoretical probability that a dart does not land in the shaded region?
8. Find the third term of the expansion (x – 2y)9.
9. Find the fourth term of the expansion (3 – siny)5.
10. Expand, (x – 2y)5 using the binomial theorem.
11. While you are at the bank, the teller asks you to create a new 4-digit code for your ATM card. Digits may repeat, but the
first number cannot be 1. How many different codes could you make for this card?
12. A survey of the soda drinking habits of the population in a high school revealed the mean number of cans of soda
consumed per person per week to be 20 with a standard deviation of 3.6. If a normal distribution is assumed, answer the
following questions.
a) Find an interval that the total number of cans per week approximately 95% of the population of this school will drink.
b) If 2800 students were surveyed, how many of them drink in between 11 and 20 cans of soda per week?
c) What percentile is a student in who drinks an average of 16.4 cans of soda per week?
13. Solve for all values of x and express in interval notation: x 3  2 x 2  9 x  2  20
3
1
b
14. Simplify:
6 9
1  2
b b
15. Solve for x:
x
9
50

 2
x  5 x  5 x  25
16. Solve for x and check your solution(s): log 9 x  log 9 ( x  8)  1
17. Given the sequence: 2, -6, 18, -54
a) Write the sum in Sigma notation
b) Find the sum
c) Find the 8th term
b) 4ln4x = 18
c)  
18. Solve each equation for x:
a) 2 x  2  3  15
1 x
1
1
 3
 9x