An urn contains a red ball, a blue ball, an orange ball, and a yellow ball. A ball is chosen one at a time then replaced. This is done 4 times. What is the probability one of each color is chosen?
To find the probability of choosing one ball of each color in 4 draws with replacement, we need to determine the total number of possible outcomes and the number of favorable outcomes.
Total number of possible outcomes:
For each draw, there are 4 different balls to choose from, so the total number of possible outcomes after 4 draws is 4 * 4 * 4 * 4 = 4^4 = 256.
Number of favorable outcomes:
To have one ball of each color in the 4 draws, we need to consider all possible combinations of selecting one ball from each color. Since all balls are replaced after each draw, the order of the colors chosen does not matter. We can calculate the number of favorable outcomes by multiplying the number of choices for each color:
Number of choices for red = 4 (since there is only one red ball)
Number of choices for blue = 4
Number of choices for orange = 4
Number of choices for yellow = 4
So, the number of favorable outcomes is 4 * 4 * 4 * 4 = 256.
Probability:
The probability of an event is calculated by dividing the number of favorable outcomes by the total number of possible outcomes.
Probability = Number of favorable outcomes / Total number of possible outcomes
Probability = 256 / 256 = 1
Therefore, the probability of choosing one ball of each color in 4 draws with replacement is 1, or 100%.