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?

There are 10x10 or 100 ways to draw the two cards

Of those the following add up to 9
1 8, 2 7, 3 6, 4 5, 5 4, 6 3, 7 2, and 8 1

so the prob of drawing 2 cards that add up to 9 is
8/100 = 2/25

Where can I play this game ?????

2+7=9 7+2=9 1+8=9 8+1=9 3+5+1=9 5+1+3=9

To determine the chance that your two cards will have a sum of nine, we need to calculate the probability for each possible combination of cards that satisfies this condition.

Before diving into the calculations, let's first identify the combinations that result in a sum of nine:
1. (3, 6)
2. (4, 5)
3. (5, 4)
4. (6, 3)

Now, we can calculate the probability for each combination by multiplying the probability of drawing each individual card.

To find the probability of drawing a specific card, we use the following formula:
Probability = (Number of favorable outcomes) / (Total number of possible outcomes)

Here's how we calculate the probability for each combination:

1. (3, 6):
Probability of drawing a 3: 1/10
Probability of drawing a 6: 1/10
Total probability = (1/10) * (1/10) = 1/100

2. (4, 5):
Probability of drawing a 4: 1/10
Probability of drawing a 5: 1/10
Total probability = (1/10) * (1/10) = 1/100

3. (5, 4):
Probability of drawing a 5: 1/10
Probability of drawing a 4: 1/10
Total probability = (1/10) * (1/10) = 1/100

4. (6, 3):
Probability of drawing a 6: 1/10
Probability of drawing a 3: 1/10
Total probability = (1/10) * (1/10) = 1/100

Since there are four possible combinations that satisfy the condition, we add up the probabilities for all four combinations:
(1/100) + (1/100) + (1/100) + (1/100) = 4/100 = 1/25

Therefore, the chance of drawing two cards with a sum of nine is 1/25.