# Probability using counting rules

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1) The waiting room for jury selection has 40 women and 30 men to choose from. A jury of 12 is selected from these 60 people, what is the probability that exactly 5 of the jury members will be women?

2) there are 48 raincoats fro sale at a local men's clothing store. Twelve are black. If six raincoats are selected to be marked down, what is the probability that more than three coats will be black?

3) What is the probability of getting a full house in a 5 card poker hand? (Full house is a 3 of a kind and a pair on any order, ie. 666kk is a full house.)

4) The powerball lottery is played twice a week in 23 states, the virgin islands and the district of Columbia. To play powerball a participant must purchase a ticket for $1 and then select five numbers from the digits 1 through 55 and a powerball number from the digits 1 through 42. To determine the winning numbers for each game, lottory officials draw five white balls out of a drum with 55 white balls and one red ball out of a drum with 42 red balls. To win the jackpot, a participant's numbers must match the numbers on the five white balls in any order and the number on the red powerball. If a person only matches the five white balls, but not the powerball they win $200,000.

a) Compute the number of ways to select the five white balls.

b) What is the probability of winning a prize of $200,000 by matching the numbers on the five white balls.

c) What is the probability of winning the powerball jackpot?

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##### Solution Summary

The solution answers four probability questions. One is on the powerball lottery, another on raincoats, another on a poker hand, and the last is on choosing people for a jury.

###### 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!"
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