Math 110 Exam I Past Exam Problems

``Math 110 Exam I Past Exam Problems

1)At a small four-year college, all freshmen and sophomores are required to enroll in exactly one of the following math classes: Math I, Math II or Math III. 200 freshmen and 450 sophomores are enrolled in Math I, 350 freshmen and 400 sophomores are enrolled in Math II, and 250 freshmen and 300 sophomores are enrolled in Math III. Find the probability that a randomly chosen person is either a freshman or enrolled in Math II

2)A student experiences difficulties with malfunctioning alarm clocks. Instead of using one alarm clock, he decides to use four. What is the probability that all four alarm clocks fail if each clock has a 95% chance of working correctly?

3) When 5 dice are rolled, how many different outcomes are possible?

4).A magazine editor must choose 4 short stories for this month’s issue from 30 submissions. In how many ways can the editor choose this month’s stories?

5)When five cards are drawn without replacement from a standard deck of 52 cards, find the probability of obtaining exactly two kings.

6)Find the probability of selecting six winning numbers from 1 to 51.

7)

The following table data are characteristics of voting-age population regarding a recent election.

When a person is chosen at random, find the probability that the person is female or voted.

8)65 percent of residents in Greenville, PA are women. When 3 people are selected at random, find the probability that all three people selected men.

9)A) How many different area code 909 telephone numbers are possible?(you may assumethat the first digit of any phone number cannot be 0 or 1) B) Suppose a computer requires eight characters for a password. The first three characters must be letters and the remaining five characters must be numbers. How many passwords are possible?

10)In how many ways can 8 people be arranged for a photograph session?

11)Suppose 40 cars start at a car race. How many ways can the top three cars finish the race?

12)A machine has a probability 0.03 of producing a defective golf ball. When 3 golf balls are manufactured by this machine, find the probability that none of the golf balls is defective.

13)How many different outcomes are possible when 3 dice and 2 coins are tossed?

14)A recent study finds that 34% of adult American males are Republicans. Based on this study, what is the probability that all 3 are Republicans when 3 adult American males are chosen randomly?

15) How many different social security numbers with the last four digits 1234 are possible?

16)From a group of 80 people, a jury of 12 people is selected. In how many ways can a jury of 12 people be selected?

17)What is the probability that your poker hand contains exactly two hearts and exactly one spade?

18) A coin is flipped 3 times. A) write out the sample space. B) Find the probability of observing two or more tails.

Answers

1)

1)

2)There is a 1-0.95=0.05 probability that an alarm clock fails. Since there are four of them, multiply this number four times to get

3)(make 5 boxes. There are 6 possible outcomes for each die.)

4) ( without replacement, the order does not matter)

5) You must choose 2 kings and 3 non-kings. There are four kings and 48 non-kings.

6)

7)

8)The probability of choosing a men is 1-0.65=0.35. Since you are choosing 3 people, multiply this number three times to get

9) (the order matters, with replacement: use the counting principle. Make 7 boxes, the first digit must be 2-9 so there are only 8 choices. ) b)

10)This is permutation: the order matters (different order produces different pictures and without replacement). 8(7)(6)…(1) = 40320 or

11)or use permutation since the order matters (tfirst place, second place, third place) and without replacement

12) The probability of a golfball not defective is 1-0.03-=0.97. Then multiply this number three times).

13)use the counting principle: the order matters, with replacement: 6 possible outcomes for a die, 2 for a coin,

14)(0.34)3

15)(10)5 (make nine boxes: the first five digits have 10 possible choices each, the last four have one choice each)

16) First observe that the selections are made without replacement and the order does not matter. So use combination:

17) (choose 2 hearts , 1 spade, and 2 others)

18)

a)HHH, HHT,HTH, HTT, THH, THT, TTH, TTT

b)There are 4 ways to observe 2 or more tails: HTT, TTH, THT, TTT: