Four blue socks, four white socks, and four gray socks

Question

are mixed in a drawer. You pull out two socks, one at a
time, without looking.
a. Draw a tree diagram along with the possible outcomes
and the probabilities of each branch.
b. What is the probability of getting a pair of socks of
the same color?
c. What is the probability of getting two gray socks?
d. Suppose that, instead of pulling out two socks, you
pull out four socks. What is the probability now of
getting two socks of the same color?

Answer 1

a. Cannot draw diagram here.

Probability of each color = 4/12 = 1/3

b. First sock = 4/12, second sock = 3/11. Probability of events all occurring is found by multiplying individual probabilities. However, you want this for either blue, white or gray. Either-or probabilities found by adding individual probabilities.

c. First step in b above.

d. With my lack of time to respond, I'll let you do this one.

Answer 2

3/11

Answer 3

A drawer contains 4 red socks, 3 white socks, and 3 blue socks. Without looking, you select a sock at random, replace it, and select a second sock at random. What is the probability that the first sock is blue and the second sock is red