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Mathbound · Contest practice

Probability worksheet

Mixed difficulty

Name

Date

1.
Two distinct days of the week are chosen uniformly at random. What is the probability that the two days are consecutive in the calendar (where Sunday and Monday are considered consecutive)?
- A.2/7
- B.1/6
- C.1/3
- D.2/5
- E.1/7
2.
Two fair dice are rolled. Probability the sum equals $7$ ?
- A.7/36
- B.6/12
- C.6/18
- D.6/36
- E.1/6
3.
Probability that a random permutation of $\{1,2,3,4,5\}$ has no fixed points?
- A.3/8
- B.2/5
- C.1/2
- D.11/30
- E.7/20
4.
Two fair dice are rolled. Probability the sum equals $3$ ?
- A.2/36
- B.1/6
- C.3/36
- D.2/12
- E.2/18
5.
Two fair dice are rolled. Probability the sum equals $2$ ?
- A.2/36
- B.1/12
- C.1/18
- D.1/36
- E.1/6
6.
Two fair dice are rolled. Probability the sum equals $8$ ?
- A.5/18
- B.5/36
- C.1/6
- D.6/36
- E.5/12
7.
Two fair dice are rolled. Probability the sum equals $10$ ?
- A.3/12
- B.3/18
- C.3/36
- D.1/6
- E.4/36
8.
Two fair dice are rolled. Probability the sum equals $11$ ?
- A.2/36
- B.1/6
- C.3/36
- D.2/12
- E.2/18
9.
Two fair dice are rolled. Probability the sum equals $9$ ?
- A.1/6
- B.5/36
- C.4/12
- D.4/18
- E.4/36
10.
Two fair dice are rolled. Probability the sum equals $12$ ?
- A.2/36
- B.1/12
- C.1/18
- D.1/36
- E.1/6

Answer key · worked solutions

1. C. 1/3
$7$ consecutive pairs among $\binom{7}{2}=21$ . $7/21=1/3$ . $1/3$ .
2. D. 6/36
Count ordered pairs out of $36$ . $6$ favorable. $6/36$ .
3. D. 11/30
$!5/5!$ . $!5=44$ . $11/30$ .
4. A. 2/36
Count ordered pairs out of $36$ . $2$ favorable. $2/36$ .
5. D. 1/36
Count ordered pairs out of $36$ . $1$ favorable. $1/36$ .
6. B. 5/36
Count ordered pairs out of $36$ . $5$ favorable. $5/36$ .
7. C. 3/36
Count ordered pairs out of $36$ . $3$ favorable. $3/36$ .
8. A. 2/36
Count ordered pairs out of $36$ . $2$ favorable. $2/36$ .
9. E. 4/36
Count ordered pairs out of $36$ . $4$ favorable. $4/36$ .
10. D. 1/36
Count ordered pairs out of $36$ . $1$ favorable. $1/36$ .

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