Mathematics

Problem

In a college,

45\%

of the students are enrolled in the Mathematics club (event

M

). The percentage of students enrolled in the Science club (event

S

) is unknown. A recent survey shows that

70\%

of the students are enrolled in at least one of the two clubs. Assume that

M

and

S

are independent. a. (i) Determine

P(S)

. b. (ii) Find

P(M\cap S)

. c. (iii) Out of

2000

students in the college, estimate how many are expected to be enrolled in both clubs, showing all calculations.