Question

3. Josh has 18 black socks and 12 white socks. Every morning he chooses one sock at random

After he has pulled that one sock out, he chooses another sock at random and wears them!
What is the probability that he...
a. first chooses a white sock, then a white sock?
b. first chooses a black sock, then a black sock?
c. first chooses a white sock, then a black sock?
d. first chooses a black sock, then a white sock?
e. gets a matching pair?
f. gets a mismatching pair?

Answer 1

According to your question, Let's calculate the probabilities for each case: (The "P" Given beside stands for Probability)

a. Probability of first choosing a white sock, then a white sock:

P(white, white) = (12/30) * (11/29) = 132/870

b. Probability of first choosing a black sock, then a black sock:

P(black, black) = (18/30) * (17/29) = 306/870

c. Probability of first choosing a white sock, then a black sock:

P(white, black) = (12/30) * (18/29) = 216/870

d. Probability of first choosing a black sock, then a white sock:

P(black, white) = (18/30) * (12/29) = 216/870

e. Probability of getting a matching pair (either both white or both black):

P(matching pair) = P(white, white) + P(black, black) = (132/870) + (306/870) = 438/870

f. Probability of getting a mismatching pair (one white and one black):

P(mismatching pair) = P(white, black) + P(black, white) = (216/870) + (216/870) = 432/870

Also If required you can further Simplify the Fractions
Hope the Answer Works ;)