Probability Mastery Exam Compact Test
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. 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%). Probability of selecting orange or blue?
A. 1%
B. 10%
C. 20%
D. 100%
4. If probability of brown is 30%, probability of not selecting brown?
A. 0.30
B. 0.50
C. 0.60
D. 0.70
5. 18/288 are over 75ft. 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. 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. 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. Outcomes independent?
A. Yes, no effect
B. No, deck changes
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 3 coins. Exactly 2 Heads?
A. 2
B. 3
C. 4
D. 1
13. Urn: 2R, 3B, 1Y. Probability first ball is blue?
A. 1/6
B. 1/3
C. 1/2
D. 3/5
14. Flip coin & toss die. P(H and roll > 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 visit orders are possible?
A. 25
B. 120
C. 24
D. 60
17. Which is a continuous random variable?
A. Books in bookstore
B. Lightning strikes
C. Plane speed
D. Soccer goals
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">x</td><td>0</td><td>1</td><td>2</td></tr><tr><td class="border border-slate-300 font-bold bg-slate-100">P(x)</td><td>.25</td><td>.60</td><td>.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">x</td><td>0</td><td>1</td><td>2</td></tr><tr><td class="border border-slate-300 font-bold bg-slate-100">P(x)</td><td>.30</td><td>.50</td><td>.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">x</td><td>0</td><td>1</td><td>2</td></tr><tr><td class="border border-slate-300 font-bold bg-slate-100">P(x)</td><td>.10</td><td>.80</td><td>.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">x</td><td>0</td><td>1</td><td>2</td></tr><tr><td class="border border-slate-300 font-bold bg-slate-100">P(x)</td><td>.50</td><td>.25</td><td>.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 lunch combinations (3S, 4Sa, 5D)?
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
25. 10 finalists, 3 winners. Groups?
A. 720
B. 120
C. 30
D. 1,000
Part III: Binomial Distribution
Formula:
\[ P(r) = \frac{n!}{r!(n-r)!} p^r q^{n-r} \]
26. Soccer player has a 75% success rate on penalty kicks. What is the probability that the player makes exactly four out of five penalty kicks?
27. A manufacturing plant produces light bulbs with a 5% defect rate. If a random sample of ten bulbs is selected, what is the probability that exactly one bulb is defective?
28. A student takes a multiple-choice quiz with 10 questions. Each question has four possible options, and only one is correct. If the student guesses randomly, what is the probability they get exactly three questions correct?
29. A fisherman has a 20% chance of catching a fish on any given cast. If he makes eight casts, what is the probability that he catches exactly two fish?
30. The weather forecast predicts a 30% chance of rain for each day of a 5-day vacation. What is the probability that it rains on exactly two of those days?
End of Probability Mastery Exam
