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Counting Principles and Probability : Combinations, Is the game fair? and Z-score

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In a Chinese restaurant, the menu lists 8 items in Column A and 6 items in column B. To order a dinner, the diner is told to select 3 items from column A and 2 from column B. How many dinners are possible?

Suppose a family plans 6 children, and the probability that a particular child is a girl is 1/2. Find the probability that the 6 child family has exactly 2 girls.

Suppose 2 cards are drawn without replacement from an ordinary deck of 52. Find the probability that both cards are aces.

You pay $6 to play a game where you will roll a die, with a payoff as follows: $8 for a 6, $7 for a 5, and $4 for any other result. What are your expected winnings? Is the game fair?

Find the following area under the standard normal curve: between z=-1.88 and z=2.10.

Find a z-score such that 8% of the area under the curve is to the right of z.

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Solution Summary

Combinations, "Is the game fair?" and Z-score are investigated. The solution is detailed and well presented.

Solution provided by:
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  • 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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