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