vzw Wi-Fi 8:55 PM 35% . APUS CLE : MATH328 D001 | Suppose 3 balls are chosen fro

Question

vzw Wi-Fi 8:55 PM 35% . APUS CLE : MATH328 D001 | Suppose 3 balls are chosen from an urn consisting of 5 white and 8 red balls, and the ball selected is replaced in the urn before the next selection. Let Xi = 1 if the ith ball selected is white, and let it be O otherwise What is the joint probability mass function of X1, X2? (7-8.25.1) OA. p(0,0) 34/169 p(0,1)- 50/169 p(1,0) 50/169 p(1,2)-35/169 O B. p(0,0)-40/169 p(0,1)-64/169 p(1,0)- 25/169 p(1,2)-40/169 C. p(0,0) 25/169 p(0,1-50/169 p(1,0) = 30/ 169 p1,2) 64/169 0 D. p(0,0)-64/169 p(0,1)-40/169 D(1,0)-40/169 p(1,2)-25/169

Explanation / Answer

Solution

This is nothing but probability of selection of 2 consecutive balls with replacement.

here, there is 5 white balls and 8 red balls given in an urn.

Therefore, P[Xi=1] = 5/13 and P[Xi=0] = 8/13.....where Xi is the ith ball selected.

we need to find joint probability function of X1 and X2,

i.e, P[X1=0,X2=0] = (8/13)*(8/13) = 64/169

P[X1=0,X2=1] = (8/13)*(5/13) = 40/169

P[X1=1,X2=0] = (5/13)*(8/13) = 40/169

P[X1=1,X2=1] = (5/13)*(5/13) = 25/169

So, the correct option is option D.

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