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Placement Test Practice — Probability & Combinatorics
Placement Test Practice — Probability & Combinatorics
Practice Test — 20 Questions
1. Compute $\binom{7}{2}$.
2. Compute $P(6,3)$.
3. How many 2-person committees from 8 people?
4. How many ways to arrange 4 books on a shelf?
5. A fair die is rolled. $P(\text{odd})$?
6. A card is drawn randomly. $P(\text{king})$?
7. $P(\text{not a king})$?
8. Two fair coins. $P(\text{exactly one head})$?
9. If $P(A)=0.4$ and $P(B)=0.3$, $A,B$ independent. $P(A \cap B)$?
10. $P(A \cup B)$ for the same events?
11. Bag: 3 red, 7 blue. Draw 2 without replacement. $P(\text{both red})$?
12. Expand $(x+1)^3$.
13. Pascal's: $\binom{6}{3}$ using the triangle.
14. Roll two dice. $P(\text{sum} = 11)$?
15. $E(X)$: win \$10 with prob $0.2$, lose \$2 with prob $0.8$.
16. $P(A|B) = 0.6$, $P(B) = 0.5$. Find $P(A \cap B)$.
17. How many 5-digit zip codes (digits 0–9, repeats okay)?
18. $\binom{10}{10}$?
19. A jar has 5 red, 5 green. $P(\text{red then green without replacement})$?
20. What is the sample space for flipping 2 coins?
Show Answer Key
1. $21$
2. $120$
3. $\binom{8}{2} = 28$
4. $4! = 24$
5. $3/6 = 1/2$
6. $4/52 = 1/13$
7. $48/52 = 12/13$
8. $2/4 = 1/2$
9. $0.12$
10. $0.4 + 0.3 - 0.12 = 0.58$
11. $\frac{3}{10} \cdot \frac{2}{9} = \frac{6}{90} = 1/15$
12. $x^3 + 3x^2 + 3x + 1$
13. $20$
14. $(5,6),(6,5) \to 2/36 = 1/18$
15. $10(0.2) + (-2)(0.8) = 2 - 1.6 = 0.40$
16. $0.6 \times 0.5 = 0.30$
17. $10^5 = 100{,}000$
18. $1$
19. $\frac{5}{10} \cdot \frac{5}{9} = 25/90 = 5/18$
20. $\{HH, HT, TH, TT\}$