Question

PROBLEM 2. 20 pts. An urn contains 4 Red balls and 6 Green balls. If 4 balls are taken one at a time with replacement. Find the probability that one is R. Find also the expected number of R and the standard deviation of R If 4 two balls are taken one at a time without replacement. Find the probability that only one is Red

Answer 1

a) The probability to get 1 red ball in the 4 balls selected is computed here as:
= Number of ways to select 1 red ball from 4 red balls * Number of ways to select 3 green balls from 6 green balls / Total ways to select 4 balls from 10 balls

b) The mean number of red balls drawn in the 4 balls drawn is computed here as:
= Proportion of red balls in the urn * Number of total balls drawn

= 0.4*4 = 1.6

Therefore 1.6 is the required expected number of red balls drawn.

c) Note that this is a case of hypergeometric distribution with N = 10 as the population size, n = 4 as the sample size and K = 4 as the number of successes that is number of red balls in the population.

The standard deviation of the number of red balls drawn is computed here as:

Therefore 0.8 is the required standard deviation here.