Week 5 Assignment 3: Quiz
Please answer the following problems. It is required that you SHOW YOUR WORK step by step to earn full credit.
By Day 6, complete and submit your answers to the W5: Assignment 3 Dropbox.
1. (2 pts) During the last hour, a telemarketer dialed 25 numbers and reached 7 busy signals, 3 answering machines, and 15 people. Use this information to determine the empirical probability that the next call will be answered in person.
15/25
= 0.6
2. (2 pts) If you roll a die many times, what would you expect to be the relative frequency of rolling a number less than 5?
You’d get 1, 2, 3, or 4 (out of 6)
4/6
= 2/3
A) 2 out of 3
3. (2 pts) A jar contains 4 yellow marbles, 12 green marbles, and 11 black marbles. If one marble is selected at random, what is the probability that it is not yellow?
Total = 4+12+11 = 27
Not yellow = 12+11 = 23
Prob = 23/27
= 0.85185
4. (2 pts) One card is selected at random from a standard 52-card deck of playing cards. Find the probability that the card selected is a jack.
There are 4 jacks:
4/52
= 0.0769
5. (2 pts) The odds against Thunderbolt winning the Birmingham Derby are 11:3. Find the probability that Thunderbolt wins.
p(11/3) = 1-p
14/3 p = 1
14p = 3
p = 3/14
B) 3/14
6. (4 pts) 500 tickets for prizes are sold for $2 each. Five prizes will be awarded – one for $300, one for $200, and three for $50. Steven purchases one of the tickets.
a) Find the expected value
-2 + 1/500*300 + 1/500*200 + 3/500*50
= -$0.70
b) Find the fair price of the ticket.
2-0.70 = 1.3
$1.30
7. (2 pts) Two balls are to be selected without replacement from a bag containing one red, one blue, one green, and one yellow ball. How many points are there in the sample space?
4C2 = 6 choices
8. (3 pts) A license plate is to consist of three letters followed by two digits. How many different license plates are possible if the first letter must be a vowel (a, e, i, o, u), and repetition of letters is not permitted, but repetition of digits is permitted?
5 choices for the first, 25 for the second, 24 for the third, then 10 and 10 for the digits:
5*25*24*10*10
= 300000
9. (2 pts) A man has 7 pairs of pants, 9 shirts, and 4 ties. How many different outfits can he wear?
7*9*4
= 252
10. (9 pts) A specific brand of bike comes in two frames, for males or females. Each frame comes in a choice of three colors, red, white, and blue, and with a choice of three seats, soft, medium, and hard.
a) Use the counting principle to determine the number of different arrangements of bicycles that are possible.
2*3*3
= 18
b) Construct a tree diagram illustrating all the different arrangements of bicycles that are possible.
c) List the sample space.
{mrs}, {mrm}, {mrh}, {mws}, {mwm}, {mwh}, {mbs}, {mbm}, {mbh}
{frs}, {frm}, {frh}, {fws}, {fwm}, {fwh}, {fbs}, {fbm}, {fbh}
11. (3 pts) The results of a survey for an airline are shown below
Traveler Male Female Total
Business / 47 / 72 / 119Vacation / 71 / 64 / 135
Total / 118 / 136 / 254
Use the chart to find the probability that the traveler was
a) male
118/254 = 0.4645669
b) on vacation given the traveler was female
64/136 = 0.470588
c) male given the traveler was on vacation
71/135 = 0.5259259
12. (2 pts) In how many ways can 6 instructors be assigned to six sections of a course in mathematics?
6! = 720
13. (4 pts) At an annual flower show, 7 different entries are to be arranged in a row.
a) How many different arrangements of the entries are possible?
7! = 5040
b) If the owners of the 1st, 2nd, and 3rd place entries will be awarded prizes of $100, $50, and $25 respectively, how many ways can the prizes be awarded?
7*6*5 = 210
14. (2 pts) How many different ways are there for an admissions officer to select a group of 6 college candidates from a group of 15 applicants for an interview?
15 choose 6 = 5005