Question

An urn contains n balls, b of which are blue and r of which are red. A random sample of n balls is withdrawn without replacement. Let B be the random variable denoting the number of blue balls in the sample. Find P(B):

a. 2^(-n)
b.b/n
c. b/n−r
d.n−b/n
​

Answer 1

The question seeks the probability of drawing blue balls from an urn without replacement.

Step-by-step explanation:

The question is asking to find the probability of drawing blue balls from an urn without replacement. Since the sample is taken without replacement, the draws are not independent, meaning this is not a binomial scenario. The probability cannot stay constant from one draw to the next. Specifically, the probability of drawing a blue ball on the first draw changes if a blue ball is indeed drawn and not replaced.

None of the probabilities listed in the options (2-n, b/n, b/(n−r), (n−b)/n) represent the probability of drawing a blue ball without replacement correctly. In a proper setup, the probability would need to account for the decreasing number of total and blue balls after each draw. The correct probability for the first blue ball would start at b/n and then change according to the balls remaining in the urn after each draw.