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:

Question

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

Answer 1

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!

Answer 2

2/25