A survey of 200 students recorded their preference for two co-curricular clubs: the…
MATHEMATICS · Multi-part · A Level · Mathematics · Probability · Probability
Problem
A survey of 200 students recorded their preference for two co-curricular clubs: the Science Club (event S) and the Drama Club (event D). It was found that 120 students joined the Science Club, 90 students joined the Drama Club and 50 students joined both clubs.
(i) Taking the selection of a student at random as the random experiment, write the numerical value of P(S), P(D) and P(S∩D).
(ii) Compute P(S∪D) and verify numerically that the addition rule holds for the events S and D.
(iii) In one or two sentences, explain why it is necessary to subtract P(S∩D) when calculating P(S∪D).