5. Ajar contains 4 pink marbles and 6 blue marbles. (a For Experiment X, three m

Question

5. Ajar contains 4 pink marbles and 6 blue marbles. (a For Experiment X, three marbles are taken out of the jar without replacement. Given that there is at least one blue marble in the sample, what is the probability that the sample contains marbles of both colors? (7 pts) (b) For Experiment Y, a trial consists of taking out a marble at random and if the marble is pink, it is not replaced and if the marble is blue, it is replaced. Determine the probability that the 2nd pink marble is observed on the 4th trial. pts)

Explanation / Answer

a) as only 3 marbles are taken out and number of both pink and blue marbles are greater then 3 then in no case all marbles from single color can be taken out,

hence probability that sample contains marbles of both colors =1

b)let pink marble drawn out is donated by P and blue marble drawn out is denoted by B

probability that 2nd pink marble is observed on 4th trail=P(PBBP+BPBP+BBPP)

=(4/10)*(6/9)*(6/9)*(3/9)+(6/10)*(4/10)*(6/9)*(3/9)+(6/10)*(6/10)*(4/10)*(3/9) =0.160593

please revert for any clarification required.

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