Garima and Hari were discussing their new neighbors, the Goyals. Garima........................What number did she say?

Question

Garima and Hari were discussing their new neighbors, the Goyals. Garima mentioned that she met two of the daughters, and they each had blond hair.

"I have met all of the sisters," replied Hari, "and the probability that both of the girls you met would have had blond hair, assuming you were equally likely to meet any of the sisters, is exactly 50%. Do you know how many children there are?"

After thinking for a minute, Garima asks if the family is abnormally large. When Hari replies that it is not, Garima tells him how many girls are in the family. What number did she say?

Answer 1

Blond - B
Normal - N

Case 1: 2 daughters ----- Not possible because there at least 2 daughters with Blonde hair
Case 2: 3 daughters ----- 2 Blondes and 1 Normal ---- Not possible because the probability of 2 random daughters being blonde is 33%
Case 3: 4 daughters ----- a] 2 Blondes and 2 Normal ---- required probability = 16.67%
b] 3 Blondes and 1 Normal ---- required probability = 50%
Therefore there are 4 daughters (3 Blondes and 1 Normal Daughter).