MA 132 Use of the Probability Model on Frequencies of Colors Problems I have handout and it has questions and I will attach the slides and the definition y

MA 132 Use of the Probability Model on Frequencies of Colors Problems I have handout and it has questions and I will attach the slides and the definition you need to answer the questions and I need it on word only and put the answers under each question Section 5.1 Questions
1. Determine which of the following tables of frequencies of colors of M&Ms in a bag is a probability model. For tables that are not probability models, explain why not.
2. In the bag of M&Ms represented by Table 1, which of the following is true? (Circle ALL that
apply)
(a) There are no blue M&Ms in the bag.
(b) All the M&Ms in the bag are blue.
(c) It is CERTAIN that you will choose a blue M&M when choosing an M&M from this bag.
(d) It is IMPOSSIBLE to choose a blue M&M when choosing an M&M from this bag.
3. In the bag of M&Ms represented by Table 3, which of the following is true? (Circle ALL that
apply)
(a) There are no yellow M&Ms in the bag.
(b) All the M&Ms in the bag are yellow.
(c) It is CERTAIN that you will choose a yellow M&M when choosing an M&M from this
bag.
(d) It is IMPOSSIBLE to choose a yellow M&M when choosing an M&M from this bag.
4. In the bag of M&Ms represented by Table 1, are there any colors of M&Ms that would be
considered unusual to choose? Please explain your answer.
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5. The following table represents the results of a survey conducted by the Centers for Disease
Control to determine college students? health-risk behaviors. Students were asked “How often
do you wear a seatbelt when driving a car?”
Response
Frequency
Never Rarely
118
249
Sometimes Most of the Time
345
716
Always
3093
(a) Construct a probability model for seatbelt use by filling in the table below.
Response
Probability
Never
Rarely
Sometimes
Most of the Time
Always
(b) Is it unusual for a student to never wear a seatbelt when driving in a car? Why or why
not?
6. If a basketball player shoots 3 free throws, write the sample space of possible outcomes using
S for a made free throw and F for a missed free throw. The first 2 are done for you:
{ (S,S,S), (S,S,F),
(a) If all of the outcomes are equally likely, what is the probability that the basketball player
makes exactly 2 free throws?
(b) If all of the outcomes are equally likely, what is the probability that the basketball player
makes at least 2 free throws?
7. A survey of 500 randomly selected high school students determined that 288 played organized
sports. What is the probability that a randomly selected high school student plays organized
sports?
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Section 5.2 Questions
8. Let the sample space of an experiment be given by S = {1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12}. Let
the event E = {2, 3, 4, 5, 6, 7}. Let the event F = {5, 6, 7, 8, 9}. Let the event
G = {9, 10, 11, 12}.
(a) What is the probability of event E?
(b) What is the probability of event F ?
(c) List the outcomes that are in both E and G.
(d) Are E and G mutually exclusive?
(e) Determine P (E or G).
(f) List the outcomes that are in both F and G.
(g) Are F and G mutually exclusive?
(h) Determine P (F or G).
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9. Using the table below, answer the following questions:
(a) Determine the probability that a randomly selected fatal crash involved a male.
(b) Determine the probability that a randomly selected fatal crash occurred on a Sunday.
(c) Determine the probability that a randomly selected fatal crash did NOT occur on a
Sunday.
(d) Determine the probability that a randomly selected fatal crash occurred on a Sunday
OR on a Monday.
(e) Determine the probability that a randomly selected fatal crash occurred on a Sunday
AND involved a male driver.
(f) Determine the probability that a randomly selected fatal crash occurred on a Sunday
OR involved a male driver.
(g) Would it be unusual for a fatal crash to occur on a Wednesday AND involve a female
driver? Please explain your answer.
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Section 5.3 Questions
10. Are the following pairs of events dependent or independent?
(a) E = Speeding on the interstate
F = Being pulled over by a police officer
(b) E = You get a high score on the statistics exam
F = The Washington Nationals win a baseball game
(c) E = You have blue eyes
F = Your friend has blue eyes
(d) E = Your parents both have blue eyes
F = You and all your siblings have blue eyes
11. About 13% of the population is left-handed. If two people are randomly selected, what is the
probability that both are left-handed?
12. What is the probability of flipping 5 heads in a row when flipping a coin?
13. What is the probability that a family with 5 children has all boys?
14. Would it be unusual for a family with 5 children to have all boys?
15. What is the probability that a family with 5 children have at least 1 girl?
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Section 5.4 Questions
16. Using the table below, answer the following questions.
(a) Determine the probability that a randomly selected fatal crash involved a male.
(b) Determine the probability that a randomly selected fatal crash involved a male GIVEN
that it occurred on a Sunday.
(c) Determine the probability that a randomly selected fatal crash occurred on a Sunday
GIVEN that it involved a male.
(d) Determine the probability that a randomly selected fatal crash occurred on a Sunday.
(e) Determine the probability that a randomly selected fatal crash occurred on a Friday
GIVEN that it involved a female.
(f) Determine the probability that a randomly selected fatal crash involved a male GIVEN
that it occurred on a weekend.
(g) Determine the probability that a randomly selected fatal crash occurred on a weekend
GIVEN that it involved a male driver..
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MA 132: Chapter 5 – Probability
Terminology
• Probability is the science of chance behavior. Behavior is unpredictable in the short run, but
has regular and predictable pattern in the long run.
• Experiment: a controlled operation that yields a set of results
• Outcomes: possible results of an experiment
• The sample space, S, of a probability experiment is the collection of all possible outcomes
• Event: any collection of outcomes from a probability experiment
• Probability: relative frequency of an outcome over the long run
• An event E is
– impossible if P (E) = 0
– a certainty of P (E) = 1
– an unusual event if P (E)