A candy dish contains 10 red, 10 orange, and 10 black gumdrops. A second dish contains exactly the same assortment. If you select a gumdrop from each dish, what are the chances that you will get two of the same color??
let's do the prob of 2 red
= (10/30)(10/30) = 1/9
the same is true for each of the other two colours
so prob(2 of the same colour) = 3(1/9) = 1/3
John, check your 3-23-11, 10:56am post.
To find the chances of selecting two gumdrops of the same color from the two dishes, we first need to calculate the total number of possible outcomes.
Let's start with one dish. There are 10 red, 10 orange, and 10 black gumdrops. So the total number of gumdrops in one dish is 10 + 10 + 10 = 30.
Now, since we have two identical dishes, the total number of possible outcomes is the product of the number of gumdrops in one dish with itself, which is 30 * 30 = 900.
Next, we need to calculate the number of favorable outcomes, which is the number of ways to choose two gumdrops of the same color. Since there are three different colors (red, orange, and black) and two identical dishes, we have three cases to consider:
1. Two red gumdrops: We need to choose two red gumdrops from the 10 available in each dish. The number of ways to choose two red gumdrops is given by the combination formula: C(10, 2) = 10! / (2! * (10-2)!) = 45.
2. Two orange gumdrops: Similarly, the number of ways to choose two orange gumdrops is also C(10, 2) = 45.
3. Two black gumdrops: The number of ways to choose two black gumdrops is C(10, 2) = 45.
Now, sum up the number of favorable outcomes: 45 + 45 + 45 = 135.
Finally, we can calculate the probability by dividing the number of favorable outcomes by the total number of possible outcomes: 135 / 900 = 0.15 (or 15%).
Therefore, the chances of selecting two gumdrops of the same color from the two dishes is 15%.