To win one million dollars, you must draw two cards whose sum is nine, from a stack of cards numbered through 10. After the first draw you replace the card and shuffle the stack again for the the second draw. What is the chance that your two cards will have a sum of nine.?
Wow, where can I play this game????
I will assume that 0 is not one of the cards.
number of possible pairs is 10x10 or 100
pairs which have a sum of 9 are:
18, 27, 36, 45, 54, 63, 72, and 81 or 8 of them
so prob that it will have a sum of 9 is 8/100 or 2/25
let me at this game!!!
To calculate the chance of drawing two cards whose sum is nine, we first need to determine the number of favorable outcomes and the total number of possible outcomes.
1. Number of favorable outcomes: To obtain a sum of nine, we can have the following combinations:
- Draw a card numbered 4 and then draw a card numbered 5.
- Draw a card numbered 5 and then draw a card numbered 4.
So, there are two favorable outcomes.
2. Total number of possible outcomes: Since we are drawing two cards from a stack of cards numbered through 10, there are 11 possible choices for each draw. Therefore, there are a total of 11 * 11 = 121 possible outcomes.
Now, we can calculate the chance of drawing two cards with a sum of nine by dividing the number of favorable outcomes by the total number of possible outcomes.
Chance = (Number of favorable outcomes) / (Total number of possible outcomes)
= 2 / 121
Therefore, the chance that your two cards will have a sum of nine is approximately 0.0165, or 1.65%.
To calculate the probability of drawing two cards whose sum is nine, we can start by determining the number of favorable outcomes and the number of possible outcomes.
First, we need to find out how many possible outcomes there are when drawing two cards from a stack numbered through 10. There are 11 cards in the stack (numbered 0-10), so the number of possible outcomes is 11 * 11 = 121.
Next, we need to determine the number of favorable outcomes, i.e., the number of ways to draw two cards with a sum of nine. We can break this down into cases:
Case 1: The first card is a 0, and the second card is a 9 (or vice versa). There are two possibilities: 0 and 9, or 9 and 0.
Case 2: The first card is a 1, and the second card is an 8 (or vice versa). There are two possibilities: 1 and 8, or 8 and 1.
Case 3: The first card is a 2, and the second card is a 7 (or vice versa). There are two possibilities: 2 and 7, or 7 and 2.
Case 4: The first card is a 3, and the second card is a 6 (or vice versa). There are two possibilities: 3 and 6, or 6 and 3.
Case 5: The first card is a 4, and the second card is a 5 (or vice versa). There are two possibilities: 4 and 5, or 5 and 4.
In total, there are 2 + 2 + 2 + 2 + 2 = 10 favorable outcomes.
Therefore, the probability of drawing two cards with a sum of nine is given by the number of favorable outcomes divided by the number of possible outcomes:
Probability = 10/121 ≈ 0.0826 (rounded to four decimal places)
So, the chance of drawing two cards whose sum is nine from the described stack of cards is approximately 0.0826, or 8.26%.