Posted by **Ana** on Thursday, January 28, 2010 at 10:53pm.

To win $1 million, you must draw two cards whose sum is nine from a stack of cards numbered 1 through 10. After the first draw, you replace the card and shuffle the stack again for the second draw. What is the chance that your two cards will have a sum of nine? I have to use the charts for the possibilities:

First Card

1 2 3 4 5 6 7 8 9 10

s 1

e 2

c 3

o 4

n 5

d 6

c 7

a 8

r 9

d 10

- Mathematicas -
**Reiny**, Thursday, January 28, 2010 at 11:19pm
there are 8 ways to get a sum of 9

1 8, 2 7, .... , 8,1

let's look at the prob of getting one of those pairs, the 1 8

prob of getting the 1 is 1/10.

since you are replacing the card, the prob of getting an 8 on the second draw is also 1/10

so the prob of getting the 1 8 combination is (1/10)(1/10) = 1/100

but there are 8 of those cases

so the prob of getting a sum of 9 when drawing 2 cards with replacement is 8/100 = 2/25

I want to play this game!

- Mathematicas -
**john**, Wednesday, December 21, 2011 at 11:46am
2/25

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