A bag contains ten marbles, 5 are yellow, 3 are blue and 2 are red. An experimen

Question

A bag contains ten marbles, 5 are yellow, 3 are blue and 2 are red. An experiment is carried out that consists of three trials. In each trial, a marble is drawn from the bag at random. When a yellow marble is drawn from the bag it is called a success; the removal of any other marble is a failure. After each trial, the marble is replaced.

(a) Is the experiment binomial? Justify your answer.

(b) What is the probability that no yellow marble is drawn in the three trials?

(c) What is the expected number of yellow marbles drawn in the three trials?

(d) Suppose that we made one change to the experiment, which was that we did not replace the marbles after each trial. Would this new experiment be binomial? Justify your answer.

Explanation / Answer

a) Here the experiment is Binomial, as the probability of success i.e. getting yellow marble is fixed in each trial which is 5 / 10 = 0.5. Let X be the no. of yellow balls drawn in n trials. Then X ~ Bin(n, 0.5). (Ans).

b) Here X ~ Bin (3, 0.5)

Required probability = P(X=0) = 0.125. (Ans).

c) Expected number of yellow marbles drawn in three trials = 3 * 0.5 = 1.5. (Ans).

d) The new experiment will not be Binomial since, the probability of success i.e. probability of getting yellow ball in each trial is not fixed. It will change after every trial. (Ans).

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