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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.

##### Solution Summary

This solution contains a detailed explanation of finding probabilities based on given information.

Solution provided by:
###### Education
• BSc , Wuhan Univ. China
• MA, Shandong Univ.
###### Recent Feedback
• "Your solution, looks excellent. I recognize things from previous chapters. I have seen the standard deviation formula you used to get 5.154. I do understand the Central Limit Theorem needs the sample size (n) to be greater than 30, we have 100. I do understand the sample mean(s) of the population will follow a normal distribution, and that CLT states the sample mean of population is the population (mean), we have 143.74. But when and WHY do we use the standard deviation formula where you got 5.154. WHEN & Why use standard deviation of the sample mean. I don't understand, why don't we simply use the "100" I understand that standard deviation is the square root of variance. I do understand that the variance is the square of the differences of each sample data value minus the mean. But somehow, why not use 100, why use standard deviation of sample mean? Please help explain."
• "excellent work"
• "Thank you so much for all of your help!!! I will be posting another assignment. Please let me know (once posted), if the credits I'm offering is enough or you ! Thanks again!"
• "Thank you"
• "Thank you very much for your valuable time and assistance!"

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