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Chapter 12 Review #2
The table shows the number of people in a crowd wearing different colors. Find the probabilities described
below.
Male
Female
Total
Purple
96
58
Blue
35
84
Yellow
14
63
Total
1. What is the probability that a randomly chosen person is a male?
2. What is the probability that a randomly chosen male is wearing blue?
3. What is the probability that a randomly chosen person wearing purple is a male?
Find the following probability.
4. If 3.7% of the items produced by a particular machine are defective, then what is the probability that a randomly
selected item will not be defective?
Find the probability of the following branches in the tree diagram.
10.
6.
5.
7.
0.2808
8.
11.
0.61
9.
0.3477
Three friends audition for different parts in the school’s chorus. Each student has a 31% chance of success.
12. Find the probability that all three students will not be successful.
13. Find the probability that exactly one student will be successful.
Use the Venn diagram below for numbers 14 - 17.
Females (F)
0.12
Athletes (A)
0.18
0.24
0.46
Find the probability of the following events.
14. P(F)
15. P(not F and not A)
16. P(F or A)
17. P(F and A)
Evaluate each expression.
18.
108!
106!
19.
(n  2)!
(n  2)!
20.
n
Pn 4
Suppose that you enter a contest that promises to award these prizes: 1 first place prize: $25,000, 50 second
place prizes: $5,000, 100 third place prizes: $1,000, 1000 fourth place prizes: $500. One entry is allowed per
person, and 50,000 people enter the contest.
21. Fill in the following table with the random variable and probability.
Possible Outcomes (x)
P(x)
22. Find the expected value for the above situation.
23. If the company running the contest charges $20 per entry, what kind of profit or loss will the company make on
this contest?
In science class there are 32 students.
24. If there are six desks in the front row, how many different ways are there to order the six people sitting up front?
25. What is the probability that the six people sitting in the front row are in alphabetical order?
26. The teacher wants to make groups of four students. She decides Peter has to be in the blue group, but Anthony
and Carlos cannot. How many different ways can the rest of the group be picked?
Using Pascal’s triangle and the Binomial Theorem, simplify the following.
27. ( x  3 y )
4
28. ( 2 x  y )
3
29. (2 x  3 y ) ; 8 term
10
th
30. (3x  5 y ) ; 9 term
12
th
KEY
1. 145/350 = 0.414
20. n!/(n-(n-4))! = n!/4! = n!/24
2. 35/145 = 0.24
21.
3. 96/154 = 0.623
22. $17.50 AVERAGE winnings per game
4. 1 – 0.037 = 0.963
23. ($20-$17.50)*50,000 = $125,000 profit
5. 0.39
per game
6. 0.28
24. 6P6 = 720
7. 0.72
25. 1/720
8. 0.43
26. 29C3 = 3654
9. 0.57
27. x4 – 12x3y +54x2y2-108xy3+81y4
10. 0.1092
28. 8x3+12x2y+6xy2+y3
11. 0.2623
29. 10C3 (2x)3 (-3y)7 = -2,099,520 x3y7
12. (0.69)(0.69)(0.69) = 0.3285
30. 12C4 (3x)4 (5y)8 = 1.566x1010 x4y8
13. (0.31)(0.69)(0.69) * 3 = 0.4428
14. 0.3
15. 0.46
16. 0.54
17. 0.18
18. 11,556
19. (n+2)(n+1)(n)(n-1)