to win 1 million dollars,you must draw two cards whose sum is 9 , from a stack of cards numbered 1 though 10 .After the first draw, you replace the card and shuffle the stack again for for the second draw. Wat is the chance your two cards will have a sum of nine?
Here are the possible ways to sum 9 with 2 cards.
8 + 1
7 + 2
6 + 3
5 + 4
1 + 8
2 + 7
3 + 6
4 + 5
Each pair has the probability of (1/10)^2. The probability of either-or events is determined by the sum of the individual events.
I hope this helps.
To calculate the probability of drawing two cards with a sum of nine, we need to determine the total number of possible outcomes and the number of favorable outcomes.
Total number of possible outcomes:
In this case, we draw two cards with replacement (meaning we put the first card back and shuffle before drawing the second one). For each card, we have a total of 10 options (numbered 1 through 10). So, the total number of possible outcomes is 10 * 10 = 100.
Number of favorable outcomes:
To calculate the number of favorable outcomes, we need to find all possible combinations of two cards that have a sum of nine. The possible combinations are:
- (1, 8)
- (2, 7)
- (3, 6)
- (4, 5)
- (5, 4)
- (6, 3)
- (7, 2)
- (8, 1)
So, there are 8 favorable outcomes.
Probability calculation:
The probability (P) is equal to the number of favorable outcomes divided by the total number of possible outcomes.
P = favorable outcomes / total outcomes
P = 8 / 100
P = 0.08
The probability of drawing two cards with a sum of nine is 0.08, or 8%.