A drawer contains 64 balls. Each ball is one of 8 colors, and there are 8 balls of each color. If the balls in the drawer are thoroughly mixed and you randomly choose two of them, what is the possibility that these two balls will have the same color?
Well, if you're anything like me, you'll be hoping that your luck isn't as mixed up as those balls in the drawer. But fear not, I'll help you sort this out!
Let's tackle this probability problem step by step. First, remember that there are 8 colors, and each color has 8 balls. That means there are 64 balls in total.
To find the probability of choosing two balls of the same color, we need to determine the number of favorable outcomes (two balls of the same color) and the total number of possible outcomes.
So, for the first ball, you have 64 options. After you've picked one ball, there are 63 balls remaining in the drawer. And out of that 63, there will be 7 balls of the same color as the one you picked.
Therefore, the number of favorable outcomes is 8 colors * 7 balls of the same color = 56.
Now, for the total number of possible outcomes, you have 64 options for the first ball and 63 options for the second ball (since you already picked one). So the total number of possible outcomes is 64 * 63.
To get the probability, you divide the number of favorable outcomes by the total number of possible outcomes: 56 / (64 * 63) = 1 / 9.
So, with a little probability magic, we find that the possibility of picking two balls of the same color is 1 out of 9. Good luck!
To find the probability that two randomly chosen balls will have the same color, we need to determine the total number of possible pairs of balls and the number of pairs that have the same color.
Step 1: Total number of possible pairs
Since there are 64 balls in the drawer, the total number of possible pairs is given by the combination formula: C(64, 2) which is equal to 64! / (2! * (64-2)!) = 64 * 63 / 2 = 2016.
Step 2: Number of pairs with the same color
For each color, there are 8 balls. So, the number of pairs with the same color is given by the combination formula: C(8, 2) which is equal to 8! / (2! * (8-2)!) = 8 * 7 / 2 = 28.
Step 3: Calculating the probability
The probability of two balls having the same color is the number of pairs with the same color divided by the total number of possible pairs.
Therefore, the probability is 28 / 2016 = 0.0139 or 1.39%.
To find the probability that the two randomly chosen balls will have the same color, you need to determine the total number of possible outcomes and the number of favorable outcomes.
First, let's calculate the total number of possible outcomes. When you choose the first ball, there are 64 possible choices. For the second ball, there are 63 remaining choices since you have already chosen one ball. Therefore, the total number of possible outcomes is 64 * 63.
Next, let's calculate the number of favorable outcomes, i.e., the pairs of balls that have the same color. There are 8 colors, and for each color, you have 8 balls. So, the number of ways to choose two balls of the same color is choosing 2 balls out of 8, which can be calculated using the combination formula: C(8, 2) = 8! / (2! * (8 - 2)!) = 28.
Finally, the probability that the two randomly chosen balls will have the same color is the number of favorable outcomes divided by the total number of possible outcomes: probability = favorable outcomes / total outcomes. Therefore, the probability is 28 / (64 * 63) ≈ 0.0694, which can be rounded to approximately 0.069 or 6.9%.
So, the possibility that these two balls will have the same color is approximately 6.9%.
say 8/64 are red
then probability of two red is
8/64 * 7/63 = 1/8 * 7/63
the next one is yellow, again same answer
but now twice the probability
so in the end
8 * 1/8 * 7/63
= 7/63