Student A and student B were given the following question: There are 14 balls (6
ID: 3055105 • Letter: S
Question
Student A and student B were given the following question: There are 14 balls (6 red balls, 5 blue balls and 3 green balls) in a bowl. Three balls are randomly chosen with replacement. Let X = the number of blue balls observed. Compute the variance of X. Answer from Student A: X is binomial because- 1) 3 independent identical trials. (n = 3) 2) Two outcomes: blue as success and other (red, green) as failure. 3) In each trial, P(success) = p = 5aand P(failure) = q =1- p = // Binomial random variable X = number of successes (blue) 5 V 9 Therefore, o² = npg = / = 31 or 0.689 5/14) Answer from Student B: X is hypergeometric because- There are 14 balls (i.e. N = 14) and 3 of them are chosen (n = 3). The ratio 143 > 0.05 . By the 5% rule, X should not be approximated as binomial. There are 5 blue balls in the urn (M = 5). 9 V11) 1485 or 0.5828 "NAN 14 / 13 2548 07 = n( MN-ME Student A and Student B give different answers and only one of them is right. Which one is correct? Explain your choice.Explanation / Answer
Student A is correct answer since it is with replacement model of the given problem. So we have to use binomial distribution
Suppose, if the problem has without replacement model, then we have to use Hyper Geometric distribution
Answer: Correct method - Student A