I MUST DRAW TWO CARDS WHOSE SUM IS NINE, FROM A STACK OF CARDS NUMBERED ONE THRU TEN. AFTER THE FIRST DRAW, I REPLACED THE CARD AND SHUFFLE THE STACK AGAIN FOR THE SECOND DRAW. WHAT IS THE CHANCE THAT MY TWO CARDS WILL HAVE A SUM OF NINE IF I DREW 10-TIMES.

Question

MY ANSWER IS 20 DRAWS FOR THE NUMBER NINE TO BE CHOSEN. AM I CORRECT.

Answer 1

no, your answer does not answer the question.

how many ways can you get a sum of nine.

1,8
8,1
7,2
2,7
3,4
4,3
5,2
2,5
6,3
3,6
so 10 ways you can get a nine. The probability of each way is 1/10*1/10

so the probability to do this in ten times is 10*1/100= 1/10

Answer 2

First you have to decide which numbers equal 9
8,1
1,8
7,2
2,7
3,6
6,3
4,5
5,4
There are 8 possible combinations to equal 9. The deck has 10 cards to start. And after the 1st draw there are 10 cards again. All together there are 10 X 10 = 100 combinations total.
8/100 = 4/50 = 2/25. Odds are 2 out of every 25 tries.