Question

Two balls are drawn in succession without replacement from an urn containing four red balls and three black balls. Let X be the possible outcomes drawing red balls. Find the probability mass function and mean for X

Answer 1

Let X be the random variable that denotes the number of red balls.

X = {0, 1, 2}

Sample space consist of ⁷C₂ = 21

X= 0, X^-1 (BB) = ³C₂

X= 1, X^-1 (BR) = ³C₁ × ⁴C₁ = 12

X = 2, X^-1 (RR) ⁴C₂ = 6

Values of random variable	0	1	2	Total
Number of elements in inverse image	3	12	6	21

Probability mass function

x	0	1	2
F(x)	`3/21`	`12/21`	`6/21`

Mean: `mu = "E"("X")`

= `sum x f(x)`

= `0 xx 3/21 + 1 xx 12/21 + 2 xx 6/21`

= `24/21`

= `8/7`