susan has red, blue, green, and yellow sweaters, joanne has green, red, purple, and white sweaters, diane's sweaters are red, blue, purple, and mauve, each girl ahs only one sweater of each color and will pick a sweater to wear at random what is the probability if each girl choose a differnet color?

If you know what a probablility tree is, draw it for this problem

http://www.onlinemathlearning.com/probability-tree-diagrams.html

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

Step 1: Calculate the total number of possible outcomes.
Since each girl has 4 different colors of sweaters to choose from, we can use the product rule to find the total number of possible outcomes.
For Susan, there are 4 choices.
For Joanne, there are 3 choices remaining (one color has already been chosen by Susan).
For Diane, there are 2 choices remaining (two colors have already been chosen by Susan and Joanne).
The total number of possible outcomes is 4 x 3 x 2 = 24.

Step 2: Calculate the number of successful outcomes.
To have each girl choose a different color sweater, Susan must choose one color, Joanne must choose a different color, and Diane must choose a different color than both Susan and Joanne.
For Susan, there are 4 choices.
For Joanne, there are 3 choices (one color has already been chosen by Susan).
For Diane, there are 2 choices (two colors have already been chosen by Susan and Joanne).
The number of successful outcomes is 4 x 3 x 2 = 24.

Step 3: Calculate the probability.
The probability of each girl choosing a different color sweater is the number of successful outcomes divided by the total number of possible outcomes.
Probability = Number of successful outcomes / Total number of possible outcomes.
Probability = 24/24 = 1.

Therefore, the probability that each girl chooses a different colored sweater is 1, or 100%.