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 has only one sweater of each color, and will pick a sweater to wear at random. Find each probability.

P(each girl chooses a different color)
P(each girl chooses the same color)
P(two girls choose the same color, and the third chooses a different color)
P(each girl chooses a red sweater)

To find each probability, we need to count the total number of possible outcomes and the number of favorable outcomes in each case.

Step 1: Counting the total number of possible outcomes.
Each girl can choose from 4 different colors, so the total number of possible outcomes is 4 * 4 * 4 = 64 outcomes.

Step 2: Counting the number of favorable outcomes for each probability.

Probability of each girl choosing a different color:
In this case, each girl needs to choose one of the four available colors without any repetition.

Susan has 4 choices.
Joanne has 3 choices remaining.
Diane has 2 choices remaining.

Therefore, the number of favorable outcomes is: 4 * 3 * 2 = 24.

Probability of each girl choosing the same color:
In this case, each girl needs to choose one of the four available colors, but they should all choose the same color.

Each girl has 4 choices, so the number of favorable outcomes is 4 * 1 * 1 = 4.

Probability of two girls choosing the same color and the third choosing a different color:
For this probability, we need to consider two scenarios:
1. Two girls choose the same color, and the third girl chooses a different color.
- Two girls can choose the same color in 3C2 ways (3 possible pairs).
- The third girl can choose a different color in 2 ways.
- Therefore, the number of favorable outcomes is 3 * 2 = 6.
2. The third girl chooses the same color as the other two girls who choose different colors.
- Two girls can choose different colors in 3C2 ways (3 possible pairs).
- The third girl has 1 out of the remaining 2 colors to choose from.
- Therefore, the number of favorable outcomes is 3 * 2 = 6.

Total number of favorable outcomes for this probability is 6 + 6 = 12.

Probability of each girl choosing a red sweater:
In this case, each girl needs to choose the red sweater. Since each girl has only one red sweater to choose from, the number of favorable outcomes is 1.

Step 3: Calculating the probabilities.

Probability of each girl choosing a different color:
P(each girl chooses a different color) = Number of favorable outcomes / Total number of possible outcomes
P(each girl chooses a different color) = 24 / 64 = 3 / 8

Probability of each girl choosing the same color:
P(each girl chooses the same color) = Number of favorable outcomes / Total number of possible outcomes
P(each girl chooses the same color) = 4 / 64 = 1 / 16

Probability of two girls choosing the same color and the third choosing a different color:
P(two girls choose the same color, and the third chooses a different color) = Number of favorable outcomes / Total number of possible outcomes
P(two girls choose the same color, and the third chooses a different color) = 12 / 64 = 3 / 16

Probability of each girl choosing a red sweater:
P(each girl chooses a red sweater) = Number of favorable outcomes / Total number of possible outcomes
P(each girl chooses a red sweater) = 1 / 64

Therefore, the calculated probabilities are as follows:
P(each girl chooses a different color) = 3 / 8
P(each girl chooses the same color) = 1 / 16
P(two girls choose the same color, and the third chooses a different color) = 3 / 16
P(each girl chooses a red sweater) = 1 / 64

8)>>>Write a group of 3 rows for girl names and and 7 columns for colors

Each girl chooses the same color (easiest)
The only color they can choose is red.
(1/4)^3=1/64
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9)>>>> P(two girls choose the same color, and the third chooses a different color)
for susan chooses red & another picks red: 2(1/4 * 1/4 * 3/4) =============6/64
for susan chooses red & and both others pick purple: 1/4 * 1/4 * 1/4=======1/64
for susan chooses blue & Diane picks blue: 1/4 * 1/4 * 4/4=================4/64
for susan chooses blue & and both others pick purple or red:1/4*2/4*1/4====2/64
for susan chooses green & Joanne picks green: 1/4 * 1/4 * 4/4==============4/64
for susan chooses green & and both others pick purple or red:1/4*2/4*1/4===2/64
for susan chooses yellow & and both others pick purple or red:1/4*2/4*1/4==2/64
total: 21/64
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10)>>> For each chosing a different color.
1-22/64=42/64=21/32