Probability Mastery Exam Compact Test Revised
Probability Mastery Exam
Comprehensive Unit Assessment
Name:
Date:
Part I: Probability Essentials
1. Which value cannot represent the probability of an event?
A. 0.71
B. 1/8
C. 120%
D. 0.5
2. In a sample of 375 couples, 34 share a trait. What is the probability a chosen couple shares it?
A. 0.091
B. 0.150
C. 0.250
D. 0.375
3. M&Ms: Orange (10%), Blue (10%). What is the probability of selecting orange or blue?
A. 1%
B. 10%
C. 20%
D. 100%
4. If probability of brown is 30%, what is the probability of not selecting brown?
A. 0.30
B. 0.50
C. 0.60
D. 0.70
5. 18 out of 288 arches are over 75ft. What is the estimated probability of choosing a tall arch?
A. 0.0625
B. 0.1800
C. 0.2880
D. 0.7500
6. When rolling two fair dice, are the outcomes on the two dice considered independent?
A. No, they are dependent
B. Yes, they are independent
7. What is the probability of rolling a "5" on green and a "3" on red die?
A. 2/6
B. 1/12
C. 1/36
D. 8/36
8. What is the probability of getting a sum of 7 when rolling two fair dice?
A. 1/6
B. 1/7
C. 7/36
D. 5/36
9. Draw 2 cards without replacement. Are the outcomes independent?
A. Yes, they are independent
B. No, they are dependent
10. No replacement. P(Ace first and King second)?
A. (4/52) × (4/51)
B. (4/52) + (4/51)
11. If you flip a fair coin three times, how many total sequences are possible?
A. 3
B. 6
C. 8
D. 9
12. Flip a coin 3 times. How many sequences have exactly 2 Heads?
A. 2
B. 3
C. 4
D. 1
13. Urn: 2 red, 3 blue, 1 yellow. Probability first ball drawn is blue?
A. 1/6
B. 1/3
C. 1/2
D. 3/5
14. Flip coin & toss die. P("Head" and number > "4")?
A. 1/4
B. 1/6
C. 1/12
D. 2/6
15. Guess randomly on 3 questions (4 choices). P(all 3 correct)?
A. 1/12
B. 1/64
C. 3/4
D. 1/16
Part II: Counting & Principles
16. Visit 5 cities. How many different visit orders are possible?
A. 25
B. 120
C. 24
D. 60
17. Which is a continuous random variable?
A. The number of books in a college bookstore
B. The number of lightning strikes in a park
C. The speed of an airplane during flight
D. The number of goals scored in a soccer match
18. Which probability distribution is invalid?
Option A
<table class="w-full border border-slate-400 bg-white text-center"><tbody><tr><td class="border border-slate-300 font-bold bg-slate-100 px-1">x</td><td class="border border-slate-300 px-1">0</td><td class="border border-slate-300 px-1">1</td><td class="border border-slate-300 px-1">2</td></tr><tr><td class="border border-slate-300 font-bold bg-slate-100 px-1">P(x)</td><td class="border border-slate-300 px-1">.25</td><td class="border border-slate-300 px-1">.60</td><td class="border border-slate-300 px-1">.15</td></tr></tbody></table>
Option B
<table class="w-full border border-slate-400 bg-white text-center"><tbody><tr><td class="border border-slate-300 font-bold bg-slate-100 px-1">x</td><td class="border border-slate-300 px-1">0</td><td class="border border-slate-300 px-1">1</td><td class="border border-slate-300 px-1">2</td></tr><tr><td class="border border-slate-300 font-bold bg-slate-100 px-1">P(x)</td><td class="border border-slate-300 px-1">.30</td><td class="border border-slate-300 px-1">.50</td><td class="border border-slate-300 px-1">.10</td></tr></tbody></table>
Option C
<table class="w-full border border-slate-400 bg-white text-center"><tbody><tr><td class="border border-slate-300 font-bold bg-slate-100 px-1">x</td><td class="border border-slate-300 px-1">0</td><td class="border border-slate-300 px-1">1</td><td class="border border-slate-300 px-1">2</td></tr><tr><td class="border border-slate-300 font-bold bg-slate-100 px-1">P(x)</td><td class="border border-slate-300 px-1">.10</td><td class="border border-slate-300 px-1">.80</td><td class="border border-slate-300 px-1">.10</td></tr></tbody></table>
Option D
<table class="w-full border border-slate-400 bg-white text-center"><tbody><tr><td class="border border-slate-300 font-bold bg-slate-100 px-1">x</td><td class="border border-slate-300 px-1">0</td><td class="border border-slate-300 px-1">1</td><td class="border border-slate-300 px-1">2</td></tr><tr><td class="border border-slate-300 font-bold bg-slate-100 px-1">P(x)</td><td class="border border-slate-300 px-1">.50</td><td class="border border-slate-300 px-1">.25</td><td class="border border-slate-300 px-1">.25</td></tr></tbody></table>
19. Compute the value of P(7, 2):
A. 14
B. 21
C. 42
D. 49
20. Compute the value of C(8, 3):
A. 336
B. 56
C. 24
D. 40,320
21. 3 positions, 10 candidates. How many ways to fill positions?
A. 120
B. 1,000
C. 720
D. 30
22. Deli: 3 sandwiches, 4 salads, 5 desserts. How many lunches?
A. 12
B. 60
C. 15
D. 23
23. Pair of dice. Outcomes where both are even numbers?
A. 9
B. 6
C. 12
D. 36
24. 2 separate decks. Probability of drawing two Kings?
A. 1/169
B. 16/2704
C. 8/52
D. A & B
25. 10 finalists, 3 winners. Order does not matter. Groups?
A. 720
B. 120
C. 30
D. 1,000
Part III: Binomial Distribution
Formula Reference:
\[ P(r) = \frac{n!}{r!(n-r)!} p^r q^{n-r} \]
26. Soccer player has 75% success rate. Probability exactly 4 out of 5 penalty kicks?
27. Light bulbs with 5% defect rate. n=10. Probability exactly 1 defective bulb?
28. 10 question quiz (4 options). Random guess. Probability exactly 3 questions correct?
29. 20% catch rate. 8 casts. Probability of exactly 2 fish caught?
30. 30% rain chance. 5-day trip. Probability of exactly 2 rain days?
End of Assessment