1. Draw a Venn-diagram to show the above information.
  2. Calculate the percent of students who passed in all three subjects.

Solution :

Let U be the set of total candidates whose results were surveyed in the examination.

Let M, S and C be the sets of candidates who passed in Maths, Science and Computer, respectively.

Here,
$n(U) = 100%$
$n(M) = 45%$
$n(S) = 55%$
$n(C) = 60%$
$n(M \cap S) = 20%$
$n(S \cap C) = 25%$
$n(C \cap M) = 20%$
$n(M \cup S \cup C)^c = 0$

To find: $n(A \cap B \cap C)= ?$

Using formula,

$n(U) = n(M) + n(S) + n(C) - \{ n(M \cap S) + n(S \cap S) + n(C \cap M) \} + n(M \cap S \cap C)$

$or, 100% = 45% + 55% + 60% - ( 20% + 25% + 20%) + n(M \cap S \cap C)$

$or, 100% = 160% - 65%$ + n(A \cap S \cap C)$

$or, 100% = 95% + n(A \cap S \cap C)$

$or, n(A \cap S \cap C) = 10% - 95%$

$\therefore n(A \cap S \cap C)= 5%$

Hence, the percentage of students who passed in all three subjects is 5%.

#SciPiPupil