Alice has 2 identical pairs of red shoes and 1 pair of white shoes, where a pair of shoes is one left and one right shoe of the same color.If she draws two shoes at random, what is the probability that she picks a pair? Give your answer as a reduced fraction.

Question

Alice has 2 identical pairs of red shoes and 1 pair of white shoes, where a pair of shoes is one left and one right shoe of the same color.If she draws two shoes at random, what is the probability that she picks a pair? Give your answer as a reduced fraction.

Answer 1

P(white,white) = 2/6 * 1/5 = 1/15

P(Lred,Rred) = 2/6 * 2/5 = 2/15
P(Rred,Lred) = 2/6 * 2/5 = 2/15

add 'em up

Answer 2

Thanks Steve!!

Answer 3

To determine the probability that Alice picks a pair of shoes, we need to consider the possible combinations of shoes that she can draw.

First, let's determine the total number of combinations Alice can draw. Alice has 2 identical pairs of red shoes and 1 pair of white shoes, making a total of 3 pairs of shoes. Each pair consists of a left and a right shoe. Therefore, Alice has a total of 2*3 = 6 individual shoes.

Next, let's find the number of ways Alice can draw a pair of shoes. Since Alice has 2 identical pairs of red shoes, there are 2 ways she can draw a pair of red shoes (either the left or the right shoe of a pair). Similarly, there is only 1 way she can draw a pair of white shoes.

So, the total number of ways Alice can draw a pair of shoes is 2 + 1 = 3.

Finally, we can calculate the probability by dividing the number of ways Alice can draw a pair of shoes by the total number of combinations. Therefore, the probability is 3/6.

To simplify the fraction, we can divide both the numerator and the denominator by their greatest common divisor, which is 3.

So, the reduced fraction is 1/2.

Therefore, the probability that Alice picks a pair of shoes is 1/2.

Answer 4

To find the probability that Alice picks a pair, we need to determine the total number of possible outcomes and the number of favorable outcomes.

First, let's calculate the total number of possible outcomes.

Alice has a total of 3 pairs of shoes: 2 pairs of red shoes and 1 pair of white shoes.

When Alice draws the first shoe, there are 6 possible choices: 2 red left shoes, 2 red right shoes, and 1 white left shoe and 1 white right shoe.

After Alice draws the first shoe, there is 1 less choice for the second shoe since she already picked one. So, for the second shoe, there are only 5 possible choices left.

Thus, the total number of possible outcomes is:
6 (choices for the first shoe) × 5 (choices for the second shoe) = 30.

Now, let's calculate the number of favorable outcomes, which is the number of ways Alice can pick a pair of shoes.

Alice can only pick a pair if she picks either 2 identical red shoes or 2 identical white shoes.

For the red shoes, the number of ways she can pick 2 identical red shoes is:
2 (choices for the first red shoe) × 1 (choice for the second red shoe) = 2.

For the white shoes, the number of ways she can pick 2 identical white shoes is:
1 (choice for the first white shoe) × 1 (choice for the second white shoe) = 1.

So, the number of favorable outcomes is 2 (for the red shoes) + 1 (for the white shoes) = 3.

Therefore, the probability that Alice picks a pair is:
Number of favorable outcomes / Total number of possible outcomes = 3 / 30 = 1 / 10.

Thus, the probability that Alice picks a pair is 1/10.