Statistics and Probability

PROBLEMS

(a)How many different 7-place license plates are possible if the first

2 places are for letters and the other 5 for number?

(b)Repeat part (a) under the assumption that no letter or number can be repeated in a single license plate.

Twenty workers are to be assigned to 20 different jobs, one to each job.

How many different assignments are possible?

If 4 Americans, 3 French people, and 3 British people

are to be seated in a row, how many seating arrangements

are possible when people of the same nationality must sit next to each other?

A history class contain 7 male students and 5 female students.

Find the number of ways that the class can elect:

(a) a class representative

(b) two class representatives, one male and one female

A class contains 10 students with 6 men and 4 women.

Find the number of ways:

(a) a 4-member committee can be selected from the students,

(b) a 4-member committee with 2 men and 2 women can be selected.

For each of the following, list the sample space and tell whether you think the events are equally likely.

(a) Roll two dice; record the sum of the numbers.

(b) A family has 3 children; record the genders in order of birth.

(d) Toss a coin 10 times.; record the longest run of heads.

In a large city, 70% of the households receive a daily newspaper,

and 50% of those who receive a daily newspaper have a television set.

What is the probability that a randomly selected household will be one that receives a daily

newspaper and has a television set?

A bin contains 100 balls, of which 25 are red,

40 are white, and 35 are black. If two balls are selected from the bin without replacement, what

is the probability that one will be red and one will be white?

Suppose the probability that a U.S.

resident has traveled to Canada is 0.18, to Mexico is 0.09,

and to both countries s 0.04. What is the probability that an American chosen at random has

(a) traveled to Canada but not to Mexico?

(b) traveled to either Canada or Mexico?

Employment data at a large company reveal that 72% of the workers are married, that 44%

are college graduates, and that half of the grads are married.

What is the probability that a randomly chosen worker

(a) is neither married nor a college graduate?

(b) is married but not a college graduate?

Seventy percent of kids who visit a doctor have fever, and 30% of kids with fever have sore throats.

What is the probability that a kid who goes to the doctor has a fever and a sore throat?

You pick three cards at random from a deck. Find the probability of each event described below.

(a) You get no aces.

(b) You get all hearts.

(d) You have at least one diamond.

There are 90 applications for a job with the news department of a television station.

Some of them are college graduates and some are not, some of them have

at least three years' experience and some have not, with the exact breakdown being:

In the order in which the applicants are interviewed by

the station manager is random, G is the event that the first applicant

interviewed is a college graduate, and T is the event that the first applicant

interviewed has at least three years' experience, determine

Given the table below, are high blood pressure and high cholesterol independent? Explain.

Suppose that 23% of adults smoke cigarettes. It is known that 57% of smokers and 13%

of nonsmokers develop a certain lung condition by age 60.

(a) Explain how these statistics indicate that lung condition and smoking are not independent.

(b) What is the probability that a randomly selected 60-year-old has this lung condition?

29 / 11

Back