Question

In a box, there are 400 blue marbles and 100 red marbles. When 200 marbles are randomly chosen from the box, let the random variable X represent the number of chosen blue marbles.

(a) Find P(X ≥ 102). [You may leave the answer in terms of “combinations” or “factorials”.]

(b) Find P(X = 160) using binomial approximation.

Answer 1

The probability of selecting a blue marble is

The probability of selecting a red marble is = 0.20

a) The probability that X will be greater than or equal to 102 is

Using the normal approximation, the expected number of blue balls out of 200 is = 0.80 * 200 = 160

The variance of the number of blue balls out of 200 is

= 0.80 * 0.20 * 200 = 32

The probability that X will be greater than or equal to 102 is

b) Using binomial approximation, the probability that X will be 160 is

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