Sally has seven blue socks and three white socks in a drawer. She picks out two socks without looking. What is the probability that both socks will be blue?

What is 7/10*6/9 ?

There are choose(10,2) = 45 ways to choose two things from ten if order doesn't matter.

There are choose(7,2) = 21 ways to choose two blue socks.

So 21/45 = 7/15

(This is the same answer as Bob's... do you see why?)

To find the probability that both socks will be blue, we need to know the total number of possible outcomes and the number of favorable outcomes.

Total number of possible outcomes:

To calculate the total number of possible outcomes, we need to consider the number of ways Sally can choose any two socks from the total number of socks in the drawer.

Since Sally has a total of 7 blue socks and 3 white socks, she has a total of 10 socks in the drawer. So, the total number of possible outcomes is the number of ways to choose 2 socks out of the 10 socks, which can be calculated using the combination formula:

Total number of possible outcomes = C(10, 2) = 10! / (2!(10-2)!) = 10! / (2! * 8!) = (10 * 9) / (2 * 1) = 45

Favorable outcomes:

The favorable outcomes are the number of ways Sally can choose 2 blue socks from the 7 blue socks. This can be calculated using the combination formula:

Favorable outcomes = C(7, 2) = 7! / (2!(7-2)!) = 7! / (2! * 5!) = (7 * 6) / (2 * 1) = 21

Probability:

Now that we know the total number of possible outcomes (45) and the number of favorable outcomes (21), we can calculate the probability of selecting two blue socks:

Probability = Favorable outcomes / Total number of possible outcomes = 21 / 45 = 0.4667 (rounded to four decimal places) or approximately 46.67%

So, the probability that Sally will select two blue socks without looking is approximately 0.4667 or 46.67%.