## MATH 399N Week 3 MyStatLab Homework Solutions: Section 3.1, 3.2, 3.3

**1. Question: 3.1.27 **The access code for a car’s security system consists of the digits. The first digit cannot be 6 and the last digit must be even. How many different codes are available? (Note that 0 is … an even number.)

**2. Question: 3.1.32 **A probability experiment consists of rolling a 6-sided die. Find the probability of the event below. Rolling a number less than 6.

**3. Question: **Use the frequency distribution to the right, which shows the number of voters (in millions) according to age, to find the probability that voter chosen at random is in the given age range. Not between 18 to 20 years old.

**4. Question: **Determine whether the following statement is true or false. If it is false, rewrite it as a true statement.

If two events are independent, P(A|B) = P(B).

**5. Question: 3.2.7 **The table below shows the number of male and female students enrolled in nursing at a particular university for a recent semester.

- Find the probability that randomly selected student is male, given that the student is a nursing major.
- Find the probability that randomly selected student is nursing major, given that the student is male.

**Nursing Majors Non-nursing majors Total**

** **

** Males **96 1120 1216

**Females **723 1688 2411

** Total **819 2808 3627

- Find the probability that a randomly selected student is male, given that the student is a nursing major.
- Find the probability that a randomly selected student is a nursing major, given that the student is male.

**6. Question: **The table below shows the results of a survey in which 143 men and 145 women workers ages 25 to 64 were asked if they have at least one month’s income set aslde for emergencies. Complete parts (a) through (d).

** Men Women Total**

** **

**Less than one month’s Income **66 83 149

**One month’s income or more **77 62 130

** Total **143 145 288

- Find the probability that a randomly selected workers has one month’s income or more set aside for emergencies.
- Given … worker is a male. Find the probability that the worker has less than one month’s income.
- Given that the randomly selected worker has one month’s income or more., find the probability that the worker is a female.
- Are the events “having less than one month’s income saved” and “being male” independent? Find the probability that a randomly selected student is a nursing major, given that the student is male.

**7. Question: **Determine whether the events E and F are independent or dependent. Justify your answer.

- E: A person attaining a position as a professor.

F: The same person attaining a PhD.

- E: A randomly selected person accidently killing a spider.

F: A different randomly selected person accidently swallowing a spider.

- E: The consumer demand for synthetic diamond.

F: The amount of research funding for diamond synthesis.

**8. Question: **In the general population, one woman in ten will develop breast cancer. Research has shown that 1 woman in 550 carries a mutation of the BRCA gene. Eight out of 10 women with this mutation develop breast cancer.

- Find the probability that a randomly selected woman will develop breast cancer given that she has a mutation of the BRCA gene.
- Find the probability that a randomly selected woman will carry the gene mutation of the BRCA gene and will develop breast cancer.

**9. Question: **In a sample of 1000 U.S. adults,211 dine out a restaurant more than once per week. Two U.S. adults are … from the population of all U.S. adults without replacement. Assuming the sample is representative of all U.S. adults, complete the parts (a) through (d).

- Find the probability that both adults dine out more than one per week.
- …. neither adult dines out more than once per week.
- Find the probability that at least one of the two adults dines out more than once per week.
- Which of these events can be … unusual? Explain. Select all that apply.

**10. Question: **According to a survey, 50% of the residents of a city oppose a downtown casino. Of these 50% about 6 out of 10 strongly oppose the casino. Complete parts (a) through (c).

- Find the probability that a randomly selected resident opposes the casino and strongly opposes the casino.
- Find the probability that a randomly selected resident who opposes the casino does not strongly oppose the casino.
- Would it … unusual for a randomly selected resident to oppose the casino and strongly oppose the casino? Explain.

## STATUS

**11. Question: **A standard deck of cards contains 52 cards. One card is … from the deck.

(a) Compute the probability of randomly selecting a spade or heart.

(b) Compute the probability of randomly selecting a spade or heart or club.

(c) Compute the probability of randomly selecting a six or heart

**12. Question: **The percent distribution of live multiple-delivery births (three or more babies) in a particular year for women 15 to 54 years old is shown in the pie chart. Find each probability.

- Randomly selecting a mother 30-39 years old
- …………………………………….. not 30-39 years old.
- Randomly selecting a mother less than 45 years old
- Randomly selecting a mother at least 20 years old.

**13.** **Question: 3.2.23**

In a sample of 800 U.S. adults, 186 dine out a restaurant more than once per week. Two U.S. adults are selected at random from the population of all U.S. adults without replacement. Assuming the sample is representative of all U.S. adults, complete the parts (a) through (d).

- Find the probability that both adults dine out more than one per week.
- ……………… the neither adult dines out more than once per week.
- Find the probability that at least one of the two adults dines out more than once per week.
- Which of these events can … unusual? Explain. Select all that apply.

**14. ****Question: 3.3.17**

A standard deck of cards contains 52 cards. One card is selected from the deck.

(a) Compute the probability of randomly selecting a five or eight.

(b) Compute the probability of randomly selecting a five or eight or queen.

(c) Compute the probability of randomly selecting a nine or club.