Let $\xi = \{\text{students in a school}\}$. $F = \{\text{students who play football}\}$. $B = \{\text{students who play baseball}\}$. Altogether, the school contains 240 students. 120 of the students play football. 40 of the students play baseball. 90 play football but not baseball.
(a)[2]
Complete the Venn diagram so that it shows this information.
(b)[1]
Find $n(F' \cap B')$.
(c)[1]
A student is picked at random from the school. Find the probability that this student plays baseball but not football.
(d)[3]
Two students who play baseball are chosen at random. Find the probability that both of them also play football.
Worked solution & mark scheme
This 7-mark question has a full step-by-step worked solution and mark scheme. One marking point: “A correct Venn diagram showing 90, 30, 10 and 110” …