(1 point) Consider another ubiquitous probability-course urn containing well-mix

Question

(1 point) Consider another ubiquitous probability-course urn containing well-mixed black and white balls. There are 15 balls in total, 6 white and 9 black. 4 are chosen, one at a time and at random. Let X, be 1 if the ith ball selected is white, and 0 otherwise For parts (a) and (b), assume that the balls are selected without replacement. (a) Calculate the conditional probability mass function Xi given that X2 -1. (b) Calculate the conditional probability mass function Xi given that X2 - 0. x x (110) For parts (c) and (d), assume that the balls are selected with replacement. (c) Calculate the conditional probability mass function X1 given that X2 -1. (d) Calculate the conditional probability mass function X1 given that X2 - 0.

Explanation / Answer

a)P(x1|X2(0|1) =P(first black and second whte)/P(second white) =(9/15)*(6/14)/(6/15)=9/14=0.6429

P(X1|X2 )(1|1)=P(bth white)/P(second white) =(6/15)*(5/14)/(6/15)=5/14 =0.3571

b)

a)P(x1|X2(0|0) =P(first black and second black)/P(second black) =8/14=4/7=0.5714

P(x1|X2(1|0) =P(first white and second black)/P(second black) =6/14=3/7 =0.4286

c) cause events are independent

probability =P(x1|X2(0|1) =9/15 =0.6

P(x1|X2(1|1) =6/15=0.4

d)P(x1|X2(0|0) =9/15=0.6

P(x1|X2(1|0) =6/15=0.4

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