(1 point) Consider another ubiquitous probability-course urn containing well-mix
ID: 3313908 • Letter: #
Question
(1 point) Consider another ubiquitous probability-course urn containing well-mixed black and white balls. There are 15 balls in total, 5 white and 10 black. 4 are chosen, one at a time and at random Let Xi be 1 if the ith ball selected is black, and 0 otherwise For parts (a) and (b), assume that the balls are selected without replacement (a) Calculate the conditional probability mass function X1 given that X2 1 Px, x (11)- (b) Calculate the conditional probability mass function X1 given that X2 -0 PX1x, (110) = For parts (c) and (d), assume that the balls are selected with replacement. (c) Calculate the conditional probability mass function X, given that X2 ! xx(01)- Px, x (11)- (d) Calculate the conditional probability mass function X1 given that 2-0 PXix, (010) = x,x, (10)Explanation / Answer
a)Px1|X2(0|1) =P(first ball white given second black) =P(first white and second black)/P(second black)
=P(first white and second black)/P(first white and second black+first black and second black)
=(5/15*10/14)/(5/15*10/14+10/15*9/14)=50/140=5/14
Px1|X2(1|1) =P(first black and second black)/P(first white and second black+first black and second black)
=9/14
b)
Px1|X2(0|0) =(5*4)/(5*4+10*5)=20/70=2/7
Px1|X2(1|0) =5/7
c) for independence Px1|X2(0|1) =P(0)=5/15 =1/3
Px1|X2(1|1) =P(1) =10/15=2/3
d)
Px1|X2(0|0) =P(0) =1/3
Px1|X2(1|0) =P(1) =2/3
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