Answer to Question #338808 in Statistics and Probability for johnanarchist

Question

The sample space contains 6 As and 4 Bs. What is the probablity that a randomly selected set of 3 will include 2 As and 1 B​?

Answer 1

Assuming you are sampling 3 individuals at the same time.

$P(A=1) = 4/10 = 0.4; P(B=1) = 0.6 = 1 - P(A)$

You took 3 individuals , what is the probability that 1 of them is A?

X — number of As in 3 individuals. Where P(A) = 0.4

P((A and A and B) or (A and B and A) or (B and B and A)) = $(0.4 \cdot 0.4 \cdot 0.6) \cdot 3 = 0.288$