total of 50 students from school A and B participated in exactly one

Hi Chetan,

First option is clear but for option B Why are we assuming that total number of students in school B is 50

Please help mecon this

A total of 50 students from school A and B participated in exactly one of two sports-cricket and hockey. If the probability of randomly selecting a hockey student from school B is x, is x > 3/5?

(1) 35 students participated from school A.

(2) There were a total of 12 students who played hockey.

Statement (1) ALONE is sufficient, but statement (2) alone is not sufficient.
Statement (2) ALONE is sufficient, but statement (1) alone is not sufficient.
BOTH statements (1) and (2) TOGETHER are sufficient, but NEITHER statement ALONE is sufficient.
EACH statement ALONE is sufficient.
Statements (1) and (2) TOGETHER are NOT sufficient.

The question is about selecting one student randomly and finding whether the probability that student is a hockey player from school B is more than 3/5 or not. Since there are total 50 students, so the question can be rephrased as: Out of total 50 students, are there more than 30 students who are from school B and played Hockey?

Thus our question changes to knowing about the number of school B hockey players more than 30.

Statement 1) Total 35 students participated from school A. It implies the remaining students, i.e. (50 – 35) = 15 participated from school B. Now even if all 15 students from School B played hockey, the probability won’t be greater than 3/5 as it is 15/50.

Thus statement I is sufficient alone as we know that the probability of selecting an hockey student from school B cannot be greater than 3/5.

Statement II. There are a total of 12 students who played hockey. Now even if we consider all 12 students who played hockey to be from School B, The probability (a student selected randomly to be a hockey student from school B) = 12/50 < 3/5

Thus we know that probability will not be greater than 3/5.

Statement II is sufficient alone.

PLEASE SEARCH BEFORE POSTING.

I read the question too fast, and I did not recognize that there are 2 different kinds of sports in this question.

Posted from my mobile device

The probability will be 15/50 . chetan2u made the typing mistake here when he wrote "15/20".

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