At a certain conference of 100 people there are 29 Indian women and 23 Indian men . Out of these Indian people 4 are doctor and 24 are either men or doctors . There are no foriegn doctors. The number of women doctors attending the conference is ?

Let us define the following events as:

M: Indian men

W: Indian women

D: Doctors who are Indian

So, now we have

n(M ∪ D) = 24

n(W) = 29

n(M) = 23

n(D) = 4

Total persons = 100

Consider, n(M ∪ D) = n(M) + n(D) – n(M ∩ D)

⇒ 24 = 23 + 4 – n(M ∩ D)

n(M ∩ D) = 3

⇒ Number of Indian men who are doctors = 3

But only 4 Indian people are doctors.

∴ Number of Indian women who are doctors = 4 – 3 = 1

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