Mathematical game: male or female kitten, what probability?

In the absence of more precise results, it is generally estimated that the two events have the same probability, that is to say 1/2, even if the reality may be slightly different.

Question:

Albane’s cat is expecting kittens. The vet examines him and tells him that she carries four. Béatrice and Caroline each want a male from the litter. Albane promises them. What is the probability that Albane can keep his promise?

Answer: 68.75%

The probability that the litter contains 0 or 1 single male is therefore far from negligible. In any case, we can liken the question to a heads or tails game. Battery is a kitten female, face, it’s a kitten male. If a coin is tossed, the probability of hitting a “tail” is equal to 1/2. The course of the game can be described by means of a tree.

At the first step the possible draws are P or F, each with probability 1/2 at the second we get PPPF, FP and FF, each with probability 1/4, and so on.

The probability of four tails (four females) is therefore equal to 1/16. Having three heads and one head is represented by PPPF, PPFP, PFPP, and FPPP, which is 4/16. The probability to have three or four females is therefore equal to 5/16. The probability of having at least 2 males is therefore equal to 11/16, or 68.75%.