# Gender of Children, Birth Dates, Kentucky Lottery

See attached file.

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=Ïƒ[ xâ‹…P( x)]=

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## SOLUTION This solution is **FREE** courtesy of BrainMass!

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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 children and they are all boys, what can the couple conclude?

Since the probability of having all boys is the couple can conclude that this event is very rare, with less than 1% chance of occurring.

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 Total

Birthday in June 1 29 30

Birthday not in June 11 324 335

Total 12 353 365

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?

There possible selections, ranging from 0000 to 9999.

b) What is the probability of winning?

The probability of winning is

c) If you win, what is your net profit?

Your net profit is

d) Find the expected value.

x, net profit/loss , Probability

Win $4999 0.0001 0.4999

Lose âˆ’$1 0.9999 âˆ’0.9999

So the expected value is a loss of 50 cents per game.

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