Question

An event has 50 female contestants and 13 male contestants. A random sample of 12 contestants is drawn. What is the probability that exactly it of the contestant will be female?

Answer 1

Let $X=$ the number of female contestants in a random sample of 12 contestants.

The probability that exactly $x$ of the contestant will be female is

$$P(X=x)=\dfrac{\dbinom{50}{x}\dbinom{13}{12-x}}{\dbinom{63}{12}}, x=0, 1, 2, ..., 12$$