Probability and Combinatorics Quiz

Grade 11 · Math · Quiz

10 questions on counting methods, compound probability, and conditional probability.

Questions

1. What is 5! (5 factorial)?

   1. 15
   2. 25
   3. 120
   4. 60
   Show answer

   Answer: 120

   5! = 5*4*3*2*1 = 120.

2. A 3-digit password uses digits 0-9 with no repetition. How many passwords are possible?

   1. 720
   2. 1000
   3. 30
   4. 504
   Show answer

   Answer: 720

   P(10,3) = 10*9*8 = 720 (ordered, no repetition).

3. C(6,2) = ?

   1. 30
   2. 15
   3. 12
   4. 36
   Show answer

   Answer: 15

   C(6,2) = 6!/(2!*4!) = (6*5)/(2*1) = 15.

4. A fair coin is flipped twice. What is P(both heads)?

   1. 1/2
   2. 1/4
   3. 1/3
   4. 3/4
   Show answer

   Answer: 1/4

   P(H)*P(H) = (1/2)*(1/2) = 1/4.

5. P(A) = 0.3, P(B) = 0.5, P(A and B) = 0.15. What is P(A or B)?

   1. 0.65
   2. 0.8
   3. 0.45
   4. 0.15
   Show answer

   Answer: 0.65

   P(A or B) = 0.3 + 0.5 - 0.15 = 0.65.

6. If P(A) = 0.6, what is P(A')?

   1. 0.6
   2. 0.4
   3. 1.6
   4. 0.36
   Show answer

   Answer: 0.4

   P(A') = 1 - P(A) = 1 - 0.6 = 0.4.

7. In how many ways can a president and vice-president be chosen from 10 candidates?

   1. 45
   2. 20
   3. 90
   4. 100
   Show answer

   Answer: 90

   P(10,2) = 10*9 = 90 (order matters because roles differ).

8. P(A|B) = 0.4 and P(B) = 0.25. What is P(A and B)?

   1. 0.1
   2. 0.4
   3. 0.65
   4. 0.16
   Show answer

   Answer: 0.1

   P(A and B) = P(A|B) * P(B) = 0.4 * 0.25 = 0.1.

9. A lottery draws 5 numbers from 1 to 50 (order does not matter). Which formula gives the number of combinations?

   1. C(50,5)
   2. P(50,5)
   3. 50*5
   4. 50!
   Show answer

   Answer: C(50,5)

   Order does not matter in lottery draws, so use combinations: C(50,5) = 2,118,760.

10. Two events are mutually exclusive. P(A) = 0.3, P(B) = 0.4. What is P(A or B)?

    1. 0.12
    2. 0.7
    3. 0.58
    4. 1.0
    Show answer

    Answer: 0.7

    Mutually exclusive -> P(A and B) = 0. P(A or B) = 0.3 + 0.4 = 0.7.

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