Susan has red, blue, and yellow sweaters. Joanne has green, red, and white sweaters. Diane's sweaters are red, blue, and mauve. Each girl has only one sweater of each color and will pick a sweater to wear at random. Find the probability that each girl chooses a different color.

27

School Subject is NOT what grade you are in.

Sra

To find the probability that each girl chooses a different color, we first need to determine the total number of possible outcomes.

Since there are 3 sweaters for each girl and they each choose a sweater at random, the total number of possible outcomes is:

Total number of outcomes = 3 * 3 * 3 = 27

Next, we need to determine the favorable outcomes. In this case, a favorable outcome is when each girl chooses a different color sweater.

To count the number of favorable outcomes, we can break it down by each girl's choices:

- For Susan to choose a different color than Joanne and Diane, she has 2 choices (blue or yellow).
- For Joanne to choose a different color than Susan and Diane, she also has 2 choices (green or white).
- For Diane to choose a different color than Susan and Joanne, she has 1 choice (mauve).

Now, we can find the total number of favorable outcomes by multiplying the choices for each girl:

Number of favorable outcomes = 2 * 2 * 1 = 4

Finally, we can calculate the probability of each girl choosing a different color by dividing the number of favorable outcomes by the total number of possible outcomes:

Probability = Number of favorable outcomes / Total number of outcomes = 4 / 27 ≈ 0.1481

Therefore, the probability that each girl chooses a different color sweater is approximately 0.1481 or 14.81%.