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;
(i) The same gender
(ii) Different gender
(ii) 2/3 * 1/3
(i) 1 minus that
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
I think I like your thinking.
Sorry, danbaba.
To calculate the probability of meeting students of the same or different genders, we need to consider the gender ratio given in the question.
(i) Probability of meeting two students of the same gender:
Since two-thirds of the students are female, the probability of meeting a female student on the first encounter is (2/3). After meeting the first student, there will be one less female in the pool. Now, the probability of meeting a female student on the second encounter is (1/2), as there is one less female to choose from. Therefore, the probability of meeting two students of the same gender (female) is (2/3) * (1/2) = 1/3.
(ii) Probability of meeting two students of different genders:
Similar to the previous scenario, the probability of meeting a female student on the first encounter is (2/3). However, after meeting the first student, the probability of meeting a male student on the second encounter is now (1/3), as there are only males left to choose from. Therefore, the probability of meeting two students of different genders is (2/3) * (1/3) = 2/9.
In summary:
(i) Probability of meeting two students of the same gender: 1/3
(ii) Probability of meeting two students of different genders: 2/9