Answer To: Only accept this assignment if you are absolutely certain that you can complete it. Document...
David answered on Dec 20 2021
Problem 1:
There are three traffic lights between your house and a friend’s house. As you arrive at each light, it
may be red (R), yellow (Y), or green (G).
a. List the sample space showing all possible sequences of red and green lights that could
occur on a trip from your house to your friend’s. (Example: RGG, which represents red at the
first light and green at the other two) Assume that each element of the sample space is
equally likely to occur.
Ans: Each light has 2 choices, and since there are 3 lights, there are 2^3, or 8 different
options of what they could be:
RRR
RRG
RGR
RGG
GGG
GGR
GRG
GRR
b. What is the probability that on your next trip to your friend’s house, you will have to stop
for exactly one red light?
Ans: The chances of stopping at exactly one light is 3/8, or 37.5% chance. You can see that
by looking at the first answer. Each light could be red and have the others al green. Since
there are three lights, there is 3 times in which that could happen
c. What is the probability that you will have to stop for at least one red light?
Ans: There is only one option to get through without and reds (GGG), therefore 7/8, or
87.5% chance of having to stop at at least one light.
Problem 2:
The number of people living in a hypothetical large Canadian city is reported by age groups in the
following table.
Age
Group
Population Percentage (%)
0 - 17 73,447 25
18 - 24 28,855 10
25 - 34 39,892 13
35 - 49 66,620 23
50 + 84,119 29
a. Verify the percentages reported in the table, and convert them into proportions.
Ans:
Age Group Population Percentage (%) Proportion
0 - 17 73,447 25 0.251
18 - 24 28,855 10 0.099
25 - 34 39,892 13 0.136
35 - 49 66,620 23 0.227
50 + 84,119 29 0.287
If one person is picked at random from all the people represented in the table, what is the
probability of the following events?
Total population
b. The person is between 18 and 24 years old.
Ans: Probability (The person is between 18 and 24 years old) = 0.099
c. The person is older than 17.
Ans: Probability (The person is older than 17) = 1 – Probability (the person is between 0 and
17 years) = 1 – 0.251 = 0.749
d. The person is between 18 and 24 or older than 17.
Ans: Probability (The person is between 18 and 24 or older than 17) =
Prob (person is between 18 and 24) + Prob (person is older than 17) = 0.099 + 0.749 = 0.848
e. The person is at least 25.
Ans: Probability (The person is at least 25) = 0.136 + 0.227 + 0.287 = 0.651
f. The person is not older than 24.
Ans: Probability (The person is not older than 24) = Probability (the person is between 0 and
17 years) + Probability (The person is between 18 and 24 years old) = 0.251 + 0.099 = 0.349
Problem 3:
A dataset contains information on travel behavior of male and female workers of a small office. A
total of 50 workers drive (27 males and 23 females) and 30 others use transit (14 males and 16
females).
If we randomly choose one individual,
a. What is the probability that the individual is a driver? [1]
Ans: Total number of workers = 50 + 30 = 80
Probability (individual is a driver) = 50/80 = 0.625
b. What is the probability that the individual is male? [1]
Ans: Total number of workers = 50 + 30 = 80
Male workers = 27 + 14 = 41
Probability (individual is a male) = 41/80 = 0.512
c. What is the probability that it is a male driver? [1]
Ans: Total number of drivers = 50
Probability (Individual is a male driver) = 27/50 = 0.54
d. What is the probability that it is a female or a transit user? [2]
Ans: Total number of female workers = 39
Total number of transit users = 30
Probability (Individual is a female or a transit user) = 39/80 + 30/80 – 16/30 =...