# MAT2051 Unit 4 Quiz (October 2019)

**MAT 2051 Discrete Mathematics**

**Unit 4 Quiz**

Question 1 How many different eight-bit strings begin with 100?

Answers:

a. 4.

b. 32.

c. 64.

d. 16.

Question 2 How many strings can be formed using the letters in the word router (that is, R-O-U-T-E-R)?

Answers:

a. 6!/2!

b. C(6, 1).

c. (6 1)!

d. C(1, 6).

Question 3 There are 100 processors, 30 of which are defective. If you select 20 microprocessors from these 100 microprocessors, what is the probability that you select no defective processors?

Answers:

a. C(100, 10)/C(30, 20).

b. C(100, 20).

c. C(100, 20)/C(70, 20).

d. C(70, 20)/C(100, 20).

Question 4 What is the probability of drawing a queen from a standard deck of cards?

Answers:

a. 2/52.

b. 10%.

c. 8/52.

d. 4/52.

Question 5 Assume the probability of having a boy or a girl is the same. If a family has five children, what is the probability that they are all boys?

Selected Answer:

a. 1/32.

b. 1/16.

c. 1/2 + 1/2 + 1/2 + 1/2 + 1/2.

d. 1/2.

Question 6 If using induction to prove that 5n 1 is divisible by 4 for all n e 1, which of the four choices best represents the base case, the assumption step, and a final step that can be used to prove for all n?

Answers:

a. 50 – 1,

5m – 1 is divisible by 4 for some value m < 1,

4 * 5m+1 + 5m+1 1

b. 51 – 1,

5m 1 is divisible by 4 for some value m > 1,

4 * 5m-1 + 5m-1 – 1

c. 51 – 1,

5m – 1 is divisible by 4 for some value m > 1,

4 * 5m + 5m – 1

d. 51 1,

-5m + 1 is divisible by 4 for some value m > 1,

Question 7 Two dice are rolled. What is the probability of rolling double sixes or double fives?

Answers:

a. 1/18.

b. 1/36.

c. 2/3.

d. 1/9.

Question 8 Suppose a microprocessor is chosen at random from a collection of 100. Assume 20 are Intels and 80 are AMDs. Also assume that 10 of the Intels are 2.0 GHz. What is the probability that the selected microprocessor is 2.0 GHz given that it is an Intel?

Answers:

a. 1/2.

b. 1/5.

c. 3/10.

d. 2/3.

Question 9 If m and n are even numbers, is y = m + n an even number?

Answers:

a. Yes.

b. No.

c. Not enough information.

d. None of the above.

Question 10 Assume that –> is IMPLICATION and ~ is NOT. Given that the following statements are true, what can be concluded via resolution?

P –> Q.

~Q.

Answers:

a. P.

b. Q.

c. ~P.

d. Q P.