Probability Mastery Exam Compact Test Revised Full
Probability Mastery Exam
Comprehensive Unit Assessment
Name:
Date:
Part I: Probability Essentials
1. Which of the following values cannot represent the probability of an event?
A. 0.71
B. 1/8
C. 120%
D. 0.5
2. In a random sample of 375 married couples, 34 couples shared all four personality preferences. What is the probability that a randomly chosen couple from this sample shares all four preferences?
A. 0.091
B. 0.150
C. 0.250
D. 0.375
3. Plain M&Ms have the color distribution: Orange (10%) and Blue (10%). What is the probability of selecting an orange or a blue candy?
A. 1%
B. 10%
C. 20%
D. 100%
4. If the probability of selecting a brown M&M is 30%, what is the probability of selecting a candy that is not brown?
A. 0.30
B. 0.50
C. 0.60
D. 0.70
5. In Arches National Park, 18 out of 288 arches are "75 feet and higher." Estimated probability that a chosen arch is at least 75 feet tall?
A. 0.0625
B. 0.1800
C. 0.2880
D. 0.7500
6. When rolling two fair dice (one green, one red), 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 a green die and a "3" on a 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. You draw two cards without replacement. Are the outcomes independent?
A. Yes, independent
B. No, dependent
9. (cont.) Options C and D:
C. Yes, if you shuffle afterwards
D. Only if different suits
10. Drawing two cards without replacement, what is the probability of drawing an Ace first and a King second?
A. (4/52) × (4/52)
B. (4/52) × (4/51)
C. (4/52) + (4/51)
D. 8/52
11. If you flip a fair coin three times, how many total sequences (outcomes) are possible in the sample space?
A. 3
B. 6
C. 8
D. 9
12. In the sample space of flipping a coin three times, exactly two heads?
A. 2
B. 3
C. 4
D. 1
13. An urn contains 6 identical balls: 2 red, 3 blue, and 1 yellow. What is the probability that the first ball drawn is blue?
A. 1/6
B. 1/3
C. 1/2
D. 3/5
14. You flip a coin and toss a die. Probability of "Head" and number > "4"?
A. 1/4
B. 1/6
C. 1/12
D. 2/6
15. If you guess randomly on three MC questions, what is the probability of getting all three correct?
A. 1/12
B. 1/64
C. 3/4
D. 1/16
Part II: Counting & Principles
16. A representative visits five cities. How many different visit orders are possible?
A. 25
B. 120
C. 24
D. 60
17. Which of the following is classified as a continuous random variable?
A. Books in a bookstore
B. Lightning strikes in a park
C. Speed of an airplane
D. 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 text-[11px]"><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</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 text-[11px]"><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</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 text-[11px]"><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</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 text-[11px]"><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</td><td>.50</td><td>.25</td><td>.25</td></tr></tbody></table>
19. Compute the value of P7,2:
A. 14
B. 21
C. 42
D. 49
20. Compute the value of C8,3:
A. 336
B. 56
C. 24
D. 40,320
21. There are three distinct nursing positions. If there are 10 candidates, how many ways can these positions be filled?
A. 120
B. 1,000
C. 720
D. 30
22. A deli lunch offers a choice of 3 sandwiches, 4 salads, and 5 desserts. How many different lunches can be ordered?
A. 12
B. 60
C. 15
D. 23
23. When tossing a pair of dice, how many outcomes result in both showing an even number?
A. 9
B. 6
C. 12
D. 36
24. You draw one card from each of two separate decks (52 cards each). What is the probability of drawing two Kings?
A. 1/169
B. 8/52
C. 16/2704
D. A & C
25. Lottery: 3 winners from 10 finalists. Order does not matter. How many groups?
A. 720
B. 120
C. 30
D. 1,000
Part III: Binomial Distribution
Formula Reference:
P(r) = (n! / (r!(n-r)!)) * pr * qn-r
26. A 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 options. If they guess randomly, what is the probability they get exactly three correct?
29. A local 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 Assessment
