Exam 10: Probability and Counting Techniques

A teacher asked his students, "Do you have a computer at home?" The responses are shown in the following table. If a student is selected at random, find the probability that (a)the student did not answer the question. (b)the student is a girl or answered "No." (c)the student is a boy or answered "Yes."

A single card is drawn from an ordinary 52-card deck. Find the probability of getting a 2 or a king.

How many ways can a committee of 3 people be selected from a group of 8 people?

How many ways can a person select four books, two CDs, and one DVD from ten books, twenty CDs, and five DVDs?

If a die is rolled one time, find the probability of getting a number greater than 6.

There were 7,234 single-bias hate crime offenses reported in a certain country in 2015. These crimes were divided into categories, with the following breakdown: 3,264 were based on racial bias, 1,446 on religious bias, 1,411 on sexual orientation bias, 1,065 on ethnic bias, and 48 against those with disabilities. a. Make a frequency distribution for this data Now use your frequency distribution to find the probability of each event in parts b-d. b. Crime was motivated by sexual orientation bias. c. Crime was motivated by bias against race or ethnicity. d. Crime was not motivated by bias against religion or those with disabilities e. Which type of probability (empirical or theoretical)are you using to answer these questions? Explain.

a. In how many ways can the letters in the word TEXAS be arranged? B. In how many ways can the letters in the word OHIO be arranged?

A box contains five blue, eight green, and three yellow marbles. If a marble is selected at random, What is the probability that it is not blue?

On The Price Is Right game show, to get into the showcase at the end, contestants spin a wheel with 20 equally sized spaces, numbered 5 cents, 10 cents, 15 cents, and so on, up to $1.00. If the contestant spins once, find the probability of each event below. a. $1.00 b. An amount less than 35 cents. c. An amount greater than 70 cents. d. An amount that is divisible by five.

How many 3-digit codes using the digits 0 through 9 are possible if repetitions are allowed?

A 2-lb bag of Hershey's miniatures contains 35 milk chocolate bars, 26 Krackel bars, 29 Mr. Goodbars, and 18 Special Dark bars. Set up a frequency distribution and find the probability that a bar chosen from a randomly selected bag is a. A Mr. Goodbar. b. A Krackel or Special Dark. c. Not a milk chocolate bar. (Express your answers as decimal values rounded to three places)

Of the next 33 trials on the docket in a county court, 4 are homicides, 11 are drug offenses, 7 are Assaults, and 11 are property crimes. If jurors are assigned to trials randomly, what's the probability That a given juror won't get a property crime case?

Evaluate 8!

A single card is drawn from a deck. What is the probability of getting a queen or a king?

Decide if the events are mutually exclusive. Roll a die: get a prime number (2, 3, 5), or get an even number.

The 2017 NCAA men's basketball tournament field had (among 64 teams)8 teams from the Atlantic Coast Conference, 6 from the Big Ten, 5 from the Big East, and 3 from the Big 12. If you were randomly assigned two teams in a dorm pool, find the probability that (a)Both were from the Big East. (b)The first was from the Atlantic Coast Conference and the second was from the Big 12.

Decide whether the following is a binomial experiment. Keeping track of the number of customers in a week that order wine with their meal.

A single card is drawn from a deck. Find the probability of selecting a 4 or a heart.

To win a prize, a person must select 4 numbers from 15 numbers without replacement. Find the Probability of winning if a person buys one ticket. (Note: The numbers can be selected in any order.)Round to four decimal places, if necessary.

Two dice are rolled. Find the probability of getting a sum of 3 or 8.