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# Gender of Children, Birth Dates, Kentucky Lottery

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You may use a calculator on this assignment. Please show work where applicable as this will help me when assigning partial credit.

Probability Questions

1. Find the probability of a couple having at least 1 girl among 7 children. Assume that boys and girls are equally likely and that the gender of a child is independent of any other child.

2. If the couple has seven children and they are all boys, what can the couple conclude?

3. Find the probability that a randomly selected subject has a birthday on the 26th of the month, given that the subject is born in June. That is, find P(Birthday on the 26th | June birthday).
Assume we are dealing with a 365 day year.

Birthday on the 26th Birthday not on the 26th
Birthday in June 1 29
Birthday not in June 11 324

4. Find the probability that a randomly selected subject has a birthday in June given that the subject was born on the 26th. That is find P(June birthday | Birthday on the 26th). Assume we are dealing with a 365 day year.

5. The Kentucky Lottery has a Pick 4 lottery game, you pay \$1 to select a sequence of four digits, such as 1332. If you select the same sequence of four digits that are drawn, you have a "straight" match and you win \$5000.

a) How many different selections are possible?
b) What is the probability of winning?
c) If you win, what is your net profit?
d) Find the expected value.

x, new profit P(x), Probability x . P(x)
Win
Lose
E=σ[ x⋅P( x)]=

##### Solution Summary

The probability of the gender of children, birth dates and Kentucky lottery is examined in the solution.

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You may use a calculator on this assignment. Please show work where applicable as this will help me when assigning partial credit.

Probability Questions (4 points each) - 16 points total

1. Find the probability of a couple having at least 1 girl among 7 children. Assume that boys and girls are equally likely and that the gender of a child is independent of any other child.

P(at least 1 girl)

2. If the couple has seven ...

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