Posted by **BadatStat** on Tuesday, July 3, 2012 at 6:22am.

A game at the state fair has a "guesser" guess the month of your birth. You win a prize if he misses your month by more than 2 months (for ex: if you were born in April, and he guesses February, he wins; if he guessed January, you win). For simplicity, assume that all 12 months are equally likely birth months, and that the results of all games are independent.

a. In the course of a night, the guesser has 6 players. What is the distribution of the number of players who win?

b. If the guesser has 6 players, find the probabilty that he wins more than half of those games.

Please help.. I have no idea what I'm doing T_T

- Statistics -
**Reiny**, Tuesday, July 3, 2012 at 7:41am
For any given birth-month the guesser wins by guessing the 5 months "around" that month.

e.g. if born in June, the correct choices would be

April, May, June, July , and August, which is 5 months.

Prob(guesser wins) = 5/12

prob(1 win out of 6) = C(6,1) (5/12) (7/12)^5 = ....

prob(2 wins out of 6) = C(6,2) (5/12)^2 (7/12)^4 = ..

prob(3 wins out of 6) = C(6,3) (5/12)^3 (7/12)^3 = ...

...

..

prob(6 wins out of 6) = C(6,6)(5/12)^6 = ...

b) prob (he wins more than half of the 6 games)

= (add up the prob of 4, 5, and 6 wins)

## Answer This Question

## Related Questions

- Math - Mike started a savings account by depositing $9. Each month, he deposits ...
- Statistics - There is a $2 raffle with a first prize of $10000, a second prize ...
- statistic - cientists are studying the population of a particular type to fish. ...
- Statistics - In a game you roll two fair dice. If the sum of the two numbers ...
- Finance - Here is a forecast of sales by National Bromide for the first 4 months...
- Math - At the carnival , the ring toss advertises that 3 of every 7 players win...
- statistics - A cereal company claims that 2 in every 15 boxes win a prize. What ...
- physics - The consumption of natural gas by a company satisfies the empirical ...
- computer programming - Write a C++ pogram for the following Employee Name and 12...
- Physics - At the State Fair you see people trying to win a prize at a game booth...

More Related Questions