Assignment: Week 3 Exercise
Course: Math 201(B2) Summmer 2014
1) Determine which of the following nubers could not represent the probability of an event.
Choose the correct answer
2. Identify the sample space of the probability experiment and determine the number of outcomes in the sample space
Randomly choosing a multiple of 3 between 1 and 20
3. Determine the number of outcomes in the event. Decide weather the event is a simple event or not.
You randomly select one card from a standard deck. Event C is selecting a red ace.
4. You randomly select one card from a standard deck. Event A is selecting a three. Determine the number of outcomes in event A. Then decide whether the event is a simple event or not.
The number of outcomes in the event A is —
Is event A a simple event?
5. Determine whether the statement is true or false. If it is false, rewrite it as a true statement.
If you roll a six sided die six times, you will roll an even number at least one.
Choose the correct answer below.
6. A random number generator is used to select a number from 1 to 100. What is the probability of selecting the number 123?
Choose the correct probability below.
7. Consider a company that selects employees for random drug tests. The company uses a computer to randomly select employees’ numbers that range from 1 to 5632. Find the probability of selecting a number less than 1000. Find the probability of selecting a number greater than 1000.
8. A family has four children. Use the tree diagram to answer each question.
9. You go to work for three days. Make an on-time/late tree diagram for the three days.
Choose the correct tree diagram below.
10. What is the probability that a registered voter voted in the election?
11. Use the frequency distribution, which shows the responses of a survey of college students when asked “How often do you wear a seat belt when riding in a car driven by someone else?” Find the following probabilities of responses of college students from the survey chosen at random.
12. Use the bar graph below, which shows the highest level of education received by employees of a company, to find the probability that the highest level of education for an employees chosen at random is B.
13. When two purple flowers (RB) are crossed, there are four equally likely possible outcomes for the genetic makeup of the offspring’s, red (RR), purple(RB) and blue(bb). If two purple snapdragons are crossed. What is the probability that the offspring will be (a) purple,(b) red and (c) blue?
14. Determine whether the events E and F are independent or dependent. Justify your answer.
a) E: A person having a high GPA
F: The same person being highly organized.
b) E: A randomly selected person coloring her hair black.
F: Another randomly selected person coloring her hair blond.
c) E: The war in a major oil-exporting country.
F: The price of gasoline.
15. Researcher found that people with depression are three times more likely to have a breathing related sleep disorder than people who are not depressed. Identify the two events described in the study. Do the results indicated that the events are independent or dependents?
Identify the two events. Choose the correct answer below.
Are the event independent or depedent?
16. In the general population, one woman in ten will develop breast cancer. Research has shown that 1 woman in 650 carries a mutation of the BRCA gene. Eight out of 10 women with this mutation develop breast cancer.
a. Find the probability that a randomly selected woman will develop breast cancer given that she has a mutation of the BRCA gene.
b. Find the probability that a randomly selected woman will carry the mutation of the BRCA gene and will develop breast cancer.
c. Are the events of carrying this mutation and developing breast cancer independent or dependent?
17. The table below shows the results of a survey in which 146 families were asked if they own a computer and if they will be taking a summer vacation this year.
a) Find the probability that a randomly selected family is not taking summer vacation this year.
b) Find the probability that a randomly selected family owns a computer
c) Find the probability a randomly selected family is taking a summer vacation this year given that they own a computer.
d. Find the probability a randomly selected family is taking a summer vacation this year and owns a computer.
e). Are the events of owing a computer and taking a summer5 vacation this year independent or dependent events?
18. Suppose 90% of kids who visits a doctor have a fever and 25% of kids with a fever have sore throats. What’s the probability that a kids who goes to the doctor has a fever and a sore throats.?
19. The table below shows the result of a survey in which 141 men and 145 women workers ages 25 to 64 were asked if they have at least one month ‘s income set aside for emergencies.
Complete parts (a) through (d)
(a) Find the probability that a randomly selected worker has one month’s income or more set aside for emergencies.
(b) Given that a randomly selected worker is a male, find the probability that the worker has less than one month’s income.
(c) Given that a randomly selected worker has one month’s income or more, , find the probability that the worker is a female.
(d) Are the events “having less than one month’s income saved “ and being male” independent or dependent?
20. About 19% of the population of a large country is hopelessly romantic. If two are randomly selected, what is the probability both are hopelessly romantic? What is the probability at least one is hopelessly romantic?
21. A distribution center receives shipments of a products from three different factories in the quantities of 60, 40 and 20. Three times a product is selected at random, each time without replacement. Find the probability that (a) all three products come from the third factory and (b) none of the here products come from the third factory.
22. By rewriting the formula for the multiplication rule, you can rewrite a formula for finding conditional probabilities. The conditional probability of event B occurring, given that event A has occurred, is P(B/ A) = P(A and B)/P(A). Use the information below to find the probability that a fight departed on time given that it arrives on time.
The probability that an airplane flight departs on time is 0.89.
The probability that a flight arrive on time is 0.87.
The probability that a flight departs and arrives on time is 0.82.
23. Determine whether the statement is true or false. If it is false, rewrite it as a true statement.
It two events are mutually exclusive; they have no outcomes in common.
Choose the correct answer below.
24. Decide if the events shown in the venn diagram are mutually exclusive.
Are the events mutually exclusive?
25. Decide if the events are mutually exclusive.
Event A: Randomly selecting someone who owns a car.
Event B: Randomly selecting a married male
Are the two events mutually exclusive?
26. During a 52- week period ,a company paid overtime wages for 19 weeks and hired temporary help for 9 weeks. During 5 weeks, the company paid overtime and hired temporary help.
Complete parts(a) and (b) below.
(a) Are the event” selecting a week that contained overtime wages” and selecting a week that contained temporary help wages” mutually exclusive?
(b) If an auditor randomly examined the payroll records for only one week, what is the probability that the payroll for that week contained overtime wages or temporary help wages.
27. The percent distribution of live multiple- delivery births (three or more babies) in a particular year for women 15 to 54 years old shown in the pie chart. Find each probabilty.
Pie Chart ( number of multiple Birth)
a. Randomly selecting a mother 30-39 years old.
b. Randomly selecting a mother not 30 -39 years old.
c. Randomly selcting a mother less than 45 years old.
d. Randomly selecting a mother at least 20 year old.
28. Find P(A or B or C) for the given probabilities.
P(A)=0.33, P(B)=0.23, P(C)=0.16
P(A and B) = 0.13, P(A and C) =0.03, P(B and C) = 0.07
P(A and B and C) = 0.01
29. Decide if the situation invovles permutations, combinations, or neither. Explain your resonsing.
The number of ways a three – member committee can be chosen from 10 people.
Does the situation involve permutaion , combinations or neither ? choose the correct answer below.
30. Space shuttle astronauts each consume an average of 3000 calories per day. One meal normally consists of a main dish, a vegetable dish and two different desserts. The astronauts can choose from 11 main dishes, 7 vegetable dishes and 12 desserts. How many different meals are possible?
31. Outside a home, there is an 8 –key keypad with letters A,B, C, D,E, F G & H that can be used to open the garage if the correct eight- letter code is entered. Each key may be used only once. How many codes are possible.
32. Suppose Grant is going to burn a compact disk (CD) that will contain 11 songs. In how many ways can grant arrange the 11 songs on the CD?