If it is confirmed that, two thirds of the students of a COLLEGE are female, calculate the probability that on entering the college, the first two students one meet are;

Question

(i) The same gender
(ii) Different gender

Answer 1

(ii) 2/3 * 1/3
(i) 1 minus that

Answer 2

for ii) I was thinking:

prob(same gender)
= Prob(both males) or prob(both female)
= (2/3)^2 + (1/3)^2
= 4/9 + 1/9
= 5/9

prob(different gender) = 1 - 5/9 = 4/9
or Prob(male, female) or Prob(female, male)
= (1/3)(2/3) + (2/3)(1/3)
= 4/9

Answer 3

I think I like your thinking.
Sorry, danbaba.