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# Compute a probability

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Question 1
Given two six sided dice, compute the probability of rolling a nine.

Question 2
A couple plans to have 4 children. Assuming the probability of obtaining each sex is 50% (1 in 2), find the probability of the couple getting four boys.

Question 3
An election committee of three men and four women has been formed to elect a local representative. Each of the seven members must be assigned to investigate one of seven different candidates. How many different ways can those assignments be made?

Question 4
Your state government decides to raise money by running a lottery where each ticket costs \$1.00 and you must choose four different whole numbers between 1 and 20. When four numbers between 1 and 20 are randomly selected, what is the probability of winning if you have one ticket and the winning numbers can be in any order?

Question 5
Given two six sided dice, compute the probability of rolling two "11's" in a row.

Question 6
The Kwik Klean Car Wash loses \$30 on rainy days and gains \$120 on days when it does not rain. If the probability of rain is 0.15, what is the expected value of net profit?

Question 7
The Newman Construction Company bids on a job to construct a building. If the bid is won, there is a 0.7 probability of making a \$175,000 profit and there is a probability of 0.3 that the contractor will break even. What is the expected value?

Question 8
Assume that in a binomial experiment, a trial is repeated n times. Find the probability of x successes given the probability p of success on a given trial with n = 12, x = 7 and p = 0.4. (Use Table A-1)

Question 9
Several students are unprepared for a true/false test with 50 questions, and all of their answers are guesses. Find the mean, variance and standard deviation for the number of correct answers for such students.

Question 10
A statistics professor finds that when she schedules an office hour for student help, an average of two students arrive. Find the probability that in a randomly selected office hour, the number of student arrivals is five.