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

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.