Most students in a large college study Mathematics. A teacher chooses three different students at random, one after the other.
Consider these three probabilities:
R = P(At least one of the students chosen studies Mathematics)
S = P(The second student chosen studies Mathematics)
T = P(All three of the students chosen study Mathematics)
Which of the following is true?
- AR < S < T
- BR < T < S
- CS < R < T
- DS < T < R
- ET < R < S
- FT < S < R
Show the answer and worked solution
answer · F
- AR < S < T
- BR < T < S
- CS < R < T
- DS < T < R
- ET < R < S
- FT < S < R
Compare the events rather than working out any numbers. "All three study Mathematics" implies "the second one does", which in turn implies "at least one does", and each implication is between events that are genuinely different in a large college, so the probabilities strictly increase along that chain. Hence T < S < R. The fact that most students study Mathematics is what makes the middle probability sit strictly between the other two rather than collapsing to 0 or 1.