Question

in a class of 45 students 30 opted for Mathematics and 32 opted for Biology. How many have opted for only Mathematics?​

Answer 1

Answer:

U = 60 n(M) = 30 n(B) = 32 n(M ∩ B) = 24 n(M ∪ B) = n(M) + n(B) – n(M ∩ B) = 30 + 32 – 24 = 38 n(M ∪ B)’ = n(∪) – n(M ∪ B) = 60 – 38 = 22 Only Mathematics = n(M) – n(M ∩ B) = 30 – 24 = 6 (i) P(student opted for Mathematics or Biology) = 24/60 = 2/5 (ii) P(student opted neither Mathematics nor Biology) = 22/60 = 11/30 (iii) P(student opted Mathematics but not Biology) = 6/60 = 1/10Read more on Sarthaks.com - https://www.sarthaks.com/827182/class-students-opted-for-mathematics-opted-for-biology-and-opted-both-mathematics-biology

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Answer 2

Answer:

13

Step-by-step explanation:

Let us say that the number of children who opted for math, only = x

Then, the number of students who opted for both the subjects = 30 - x

Let us say that the number of students who opted for only biology = y

Then, x + 30 - x + y = 45

y = 15

15 students opted for only Biology.

So, the number of students who opted for both the subjects = 32 - 15 = 17

Now,

30 - x = 17

x = 13