Problem # 2: Please solve step by step and clearly. Thank you. An urn contains 3

Question

Problem # 2: Please solve step by step and clearly. Thank you. An urn contains 3 green balls, 2 red balls and 1 blue ball. Experiment # 3: We draw two balls (together) from the urn at random. (a) What is the probability that both balls are red? (b) What is the probability that both balls are green? (c) Let X be the random variable that is 1 if the colors of the two balls drawn in Experiment # 3 are different. Let Y be the random variable that is 1 if the colors of the two balls drawn in Experiment # 2 are the same. Find the covariance of X and Y. (d) Interpret your answer to Part (c). (Is the answer what you would expect intuitively? Why?)

Explanation / Answer

Total number of balls is 3+2+1 = 6

Number of ways of selecting 2 balls out of 6 is C(6,2) = 15

(A)

Out of 6 balls , 2 are red so number of ways of selecting 2 red balls is C(2,2)=1

P(both red) = 1/15

(B)

Out of 6 balls , 3 are green so number of ways of selecting 2 green balls is C(3,2)=3

P(both green) = 3 /15 =0.2

(c-d) For these two parts need experiment #2

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