You have a very messy sock drawer with 3 blue socks, 5 black socks, and 1 white sock. You pick two socks from the drawer. You pick a second one without replacing the first one. Find each probability.

1) Probability of picking 2 blue socks

2) Probability of picking black than blue

I think I have to draw a certain number of blanks and then write in numbers and multiply... I am only uncertain as to what numbers I need to use..

Thanks for your help!

I will be happy to critique your thinking.

For the first one, would I take 3/9 times 2/8 because there is a 3/9 chance of picking a blue sock, but then after picking out one, there is only a 2/8 chance. So the answer for 1 is 6/72 ???

there were 6 purple socks and 4 orange socks in a drawer. Zucky picked one sock without looking and then another without looking(or replacing the first). What is the probability that he picked 2 purple socks?

To find the probability of an event, you need to divide the number of favorable outcomes by the total number of possible outcomes.

1) Probability of picking 2 blue socks:

First, let's calculate the total number of possible outcomes. When picking two socks out of the drawer without replacing the first one, there are a total of 9 socks to choose from: 3 blue socks, 5 black socks, and 1 white sock.

The number of favorable outcomes is the number of ways you can choose two blue socks from the 3 blue socks in the drawer. To choose two blue socks, you can think of it as selecting 2 out of the 3 blue socks, which is a combination.

The formula for a combination is:

nCr = n! / (r!(n-r)!)

Where n is the total number of items, and r is the number of items being selected.

Using this formula, we can calculate the number of combinations of choosing 2 out of 3 blue socks:

3C2 = 3! / (2!(3-2)!) = 3! / (2!1!) = 3

So, there are 3 different ways to choose 2 blue socks from the drawer.

Therefore, the probability of picking 2 blue socks is:

P(2 blue socks) = favorable outcomes / total possible outcomes = 3 / 9 = 1/3

2) Probability of picking black than blue:

To calculate this probability, we need to consider the order in which we pick the socks. We want to find the probability of picking a black sock first, followed by a blue sock second.

The number of favorable outcomes in this case is the number of ways you can choose 1 black sock out of the 5 black socks and 1 blue sock out of the 3 blue socks.

Using the same combination formula, we can calculate the number of combinations:

5C1 = 5! / (1!(5-1)!) = 5! / (1!4!) = 5

3C1 = 3! / (1!(3-1)!) = 3! / (1!2!) = 3

So, there are 5 different ways to select a black sock first and 3 different ways to select a blue sock second.

Therefore, the probability of picking black than blue is:

P(black than blue) = favorable outcomes / total possible outcomes = (5 * 3) / 9 = 15 / 9 = 5/3 (approximately 1.67)