# Statistics

• Apr 1st 2009, 11:29 AM
deepnthought
Statistics
A lottery involves drawing five white balls out of a drum with 55 balls and then drawing one red ball out of a drum with 42 red balls. (Hint: these are two separate events.) You can buy a $1 ticket and select five white numbers (from 1 to 55 inclusive) and one red number (from 1 to 42 inclusive). You win the lottery if you pick all five of the correct white balls and the correct red ball. (It does not matter what order the balls are drawn.) How much would you have to spend to cover all possible combinations? If the jackpot was$100 million, assuming you'd be the only winner, would this be a good idea?
• Apr 1st 2009, 12:08 PM
Soroban
Hello, deepnthought!

Quote:

A lottery involves drawing five white balls out of a drum with 55 balls
and then drawing one red ball out of a drum with 42 red balls.
(Hint: these are two separate events.)

You can buy a $1 ticket and select five white numbers (from 1 to 55 inclusive) and one red number (from 1 to 42 inclusive). You win the lottery if you pick all five of the correct white balls and the correct red ball. (It does not matter what order the balls are drawn.) (a) How much would you have to spend to cover all possible combinations? (b)If the jackpot was$100 million, assuming you'd be the only winner,
. . .would this be a good idea?

There are: . ${55\choose5}$ ways to choose five white balls
. . and ${42\choose1}$ ways to choose one red ball.

Hence, there are: . $3,\!478,\!761 \times 42 \:=\:146,\!107,\!962$ possible outcomes.

(a) It would cost you $\146,\!107,\!962$ to cover all combinations.

(b) You spend over 146 million dollars to win 100 million?
. . .Do the math!