An urn contains n + m balls, of which n are red and m are black. They are withdrawn from the urn, one at a time and without replacement. Let X be the number of red balls removed before the first black ball is chosen. We are interested in determining E[X]. To obtain this quantity, number the red balls from 1 to n. Now define the random variables

if red ball i is taken before any black ball is chosen

Otherwise

a) Express X in terms of the

b) Find E[X]

Question

Mathematics

Koen Shields

9 February, 08:13

An urn contains n + m balls, of which n are red and m are black. They are withdrawn from the urn, one at a time and without replacement. Let X be the number of red balls removed before the first black ball is chosen. We are interested in determining E[X]. To obtain this quantity, number the red balls from 1 to n. Now define the random variables

if red ball i is taken before any black ball is chosen

Otherwise

a) Express X in terms of the

b) Find E[X]

+4

Answers (1)

Know the Answer?

Dulce Shaffer · Answer 1

Answer: Let number of red balls = n

number of black balls = m

number of red and black balls = n + m

Step-by-step explanation:

a) number of n balls chosen, X = n/n+m

b) number of n balls chosen without replacement, E (X) = n/n+m*{n/n+m-1}

∴ E (X) = n²/n²+2nm+m²+n-m