In an entrance process for a professional college, 500 applicants were evaluated by…
MATHEMATICS · Multi-part · A Level · Mathematics · Probability · Probability
Problem
In an entrance process for a professional college, 500 applicants were evaluated by two tests:
A : "qualified the Aptitude Test"
I : "qualified the Interview".
The records show that 260 applicants qualified the Aptitude Test, 210 qualified the Interview, and 120 qualified both.
(i) Express, in the form of probabilities, the fractions of applicants who qualified (a) only the Aptitude Test, (b) only the Interview, (c) at least one of the two tests.
(ii) Verify numerically that the probability found in part (i)(c) satisfies the relationship among P(A), P(I) and P(A∩I).
(iii) Two applicants are selected at random without replacement. Determine the probability that both of them qualified at least one of the two tests.