11 Mid-Chapter Quiz

Do you know HOW?

Evaluate each expression.

1. 4!
2. 6!
3. 5 ! 3 ! fraction 5 factorial , over 3 factorial end fraction
4. 6 ! 4 ! 2 ! fraction 6 factorial , over 4 factorial 2 factorial end fraction
5.   7 C 3 sub 7 , cap c sub 3
6.   9 C 8 sub 9 , cap c sub 8
7.   5 P 2 sub 5 , cap p sub 2
8.   11 P 9 sub 11 , cap p sub 9
9.   4 C 4 sub 4 , cap c sub 4
10.   4 P 4 sub 4 , cap p sub 4
11. 2 (   5 C 4 ) −   3 C 2 2 open , sub 5 , cap c sub 4 , close minus , sub 3 , cap c sub 2
12. 3 (   3 P 2 ) +   3 P 1 3 open , sub 3 , cap p sub 2 , close plus , sub 3 , cap p sub 1

Indicate whether each situation involves a combination or permutation. Then solve.

13. How many ways are there to select five actors from a troupe of nine to improvise a scene?
14. How many different three-student study groups can be formed from a class of 15?
15. Your teacher is looking for a new apartment. There are five apartments available. In how many ways can your teacher inspect the apartments?

Suppose you select a number at random from the sample space {5, 6, 7, 8, 9, 10, 11, 12, 13, 14}. Find each probability.

16. P(7)
17. P(5 or 13)
18. P(greater than 10)
19. P(multiple of 30)
20. P(less than 7 or greater than 10)
21. P(greater than 6 and less than 12)
22. P(integer)
23. P(less than 10 | less than 13)
24. P(greater than 8 | less than 11)
25. P(greater than 7 | greater than 12)

Two standard number cubes are tossed. State whether the events are mutually exclusive. Then find P(A or B).

26. A means their sum is 12; B means both are odd.
27. A means they are equal; B means their sum is a multiple of 3.

Do you UNDERSTAND?

28. Vocabulary Explain the difference between experimental probability and theoretical probability.
29. Suppose you select a number at random from the set {90, 91, 92, …, 99}. Event A is selecting a multiple of 2. Event B is selecting a multiple of 3.
    1. Writing Are events A and B mutually exclusive? Are they independent? Explain your answers.
    2. Find P(A) and P(B).
    3. Find P(A and B).
    4. Find P(A or B).
    5. Find P(A | B) and P(B | A).
30. Reasoning Let F and G be mutually exclusive events. Event F occurs more frequently than event G. Write the following in order from least to greatest: P(F), P(G), P(F or G), P(G | F).

31. Error Analysis For two events A and B, a student calculates the probabilities shown. Explain how you can tell that the student made a mistake.

    

32. Open-Ended Your teacher selects at random two days out of every five days to give a “pop” quiz. Define a simulation to find the experimental probability that you will get a pop quiz on two consecutive days. Then use your simulation to find the probability.

Table of Contents