MATH 210

Exam 3

April 17, 1996

 

1. A pair of fair dice is cast. What is the probability that one of the numbers is 4 given that the sum of the numbers on the uppermost faces is 8?

(a)

1 / 36

(b)

1 / 5

(c)

1 / 3

(d)

1 / 6

(e)

None of the above.

 

2. A pair of fair dice is cast. What is the probability that one of the numbers is 4 and that the sum of the numbers on the uppermost faces is 8?

(a)

1 / 36

(b)

1 / 5

(c)

1 / 3

(d)

1 / 6

(e)

None of the above.

 

3. What is the coefficient of

in the binomial

expansion of

(a)

18

(b)

34

(c)

35

(d)

17

(e)

None of the above.

 

4. Suppose that a red die and a green die are tossed and the numbers on the uppermost faces are observed. What is the probability that the sum of the numbers is less than 3?

(a)

1 / 36

(b)

1 / 18

(c)

1 / 12

(d)

1 / 3

(e)

None of the above.

 

For the next two problems consider the following.

You ask a friend to feed your goldfish while you are on vacation.

The probability that they forget is 1/5.

If your fish is fed the probability that it will die is 1/4.

If it does not get fed, the probability that it will die is 7/8.

 

5. What is the probability that your goldfish dies?

(a)

7 / 15

(b)

3 / 8

(c)

7 / 8

(d)

9 / 16

(e)

None of the above.

 

6. Your goldfish dies. What is the probability that your friend forgot to feed it?

(a)

7 /15

(b)

3 / 8

(c)

7 / 8

(d)

9 / 16

(e)

None of the above.

 

7. A card is drawn at random from a deck of 52 playing cards. Find the probability that the card is red or a seven.

(a)

1 / 26

(b)

1 / 2

(c)

3 / 13

(d)

7 / 13

(e)

None of the above.

 

8. Two cards are selected at random from a standard deck, one at a time without replacement. Find the probability that the second is red given that the first is a seven.

(a)

1 / 26

(b)

1 / 2

(c)

3 / 13

(d)

7 / 13

(e)

None of the above.

 

9. In a class of 80 there are to be 16 A's, 12 B's, 25 C's, 13 D's and 14 F's. In how many ways can these be awarded?

(a)

C(80,16) x C(80,12) x C(80,25) x C(80,13) x C(80,14)

(b)

C(80,16) + C(80,12) + C(80,25) + C(80,13) + C(80,14)

(c)

C(80,16) x C(64,12) x C(52,25) x C(27,13)

(d)

C(80,16) + C(64,12) + C(52,25) + C(27,13)

(e)

None of the above.

 

10. If E and F are mutually exclusive events with Pr(E)=1/5 and Pr(F)=1/6 then

(a)

11 / 30

(b)

1 / 11

(c)

1 / 3

(d)

1 / 30

(e)

None of the above.

 

11. If E and F are independent events with

Pr(E)=1/5 and Pr(F)=1/6 then

(a)

44%

(b)

56%

(c)

38%

(d)

62%

(e)

None of the above. 

 

12. A bag contains nine tomatoes, of which two are rotten. A sample of three tomatoes is selected at random. What is the probability that the sample contains exactly one rotten tomato?

(a)

1 / 4

(b)

1 / 9

(c)

1 / C(9,3)

(d)

1 / 2

(e)

None of the above.

 

13. Consider the following matrices:

Which are stochastic and regular?

(a)

Y only.

(b)

V and X only.

(c)

X only.

(d)

X and Y only.

(e)

Some other selection.

 

For the next two problems consider the following:

ACE insurance company found that 30% of the drivers in Kalbville who were involved in an accident one year were also involved in an accident the following year. They also noticed that only 10% of the drivers who were not involved in an accident one year were involved in an accident the following year.

 

14. If 20% of the drivers in Kalbville are involved an accident in 1996, how many are likely to be involved in an accident in 1998?

(a)

43.2%

(b)

22%

(c)

78%

(d)

56.8%

(e)

None of the above.

 

15. In the long run, what fraction of the drivers of Kalbville are involved in an accident each year?

(a)

1 / 3

(b)

1 / 5

(c)

9 / 16

(d)

1 / 8

(e)

None of the above.

 

© Department of Mathematical Sciences, Northern Illinois University, DeKalb IL 60115 

Prepared 11/11/97 by Dr. Anders Linnér (alinner@math.niu.edu)