Question

create a word statement for the following probability event: A n B n C (so a intersects b intersects c)

Answer 1

1) In a survey of 200 students of a school it was found that 120 study mathematics, 90 study physics and 70 study chemistry, 40 study mathematics and physics, 30 study physics and chemistry, 50 study chemistry and mathematics and 20 study none of these subjects. Find the number of students who study all three subjects.

Solution :
M = Mathematics ; P = Physics and C = Chemistry

n(M) = 120 n(P) = 90 n (C) = 70 n ( M ∩ P) = 40
n ( P ∩ C ) = 30 n ( C ∩ M ) = 50 n ( M ∪ P ∪ C )’ = 20

Now n(M ∪ P ∪ C)’ = n(U) – n(M ∪ P ∪ C)

20 = 200 – n (M ∪ P ∪ C)

Therefore, n(M ∪ P ∪ C) = 200 – 20 = 180

Probability=20/200=0.1
n(M ∪ P ∪ C)
= n(M) + n(P) + n(C) – n(M ∩ P) – n(P ∩ C) – n(C ∩ M) + n(M ∩ P ∩ C)

180 = 120 + 90 + 70 - 40 - 30 - 50 + n(M ∩ P ∩ C)

⇒ n(M ∩ P ∩ C) =180 - 120 - 90 - 70 + 40 + 30 + 50

⇒ n(M ∩ P ∩ C) = 20.