Abag contains two black balls, three white balls, and four red balls. three balls are drawn at random without replacement. let y1 be the number of black balls drawn and y2 the number of white balls drawn. a) find e(y2|y1 = y1)

1/3

Step-by-step explanation:

This is an independent event i.e the occurrence of one does not affect the other

Finding E(Y2|Y1) means E(Y2) i.e probability that Y2 is selected if it is E(Y1|Y2), this means probability of drawing Y1.

Since this an independent event,

E(Y2|Y1) =E(Y2)

Since three balls are drawn at random, probability of drawing Y2 will be 3/9 i.e 1/3

Note that the sum total of the balls will be the total outcome.

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we have three similar triangles, because each has a right angle and shares an angle.   let's write the angles in order: opposite to short leg, long leg, hypotenuse.

cab similar to bad similar to cbd

or as ratios,

ca: ab: cb = ba: ad: bd = cb: bd: cd

we also know

ac = ad + cd

(ad+cd): ab: cb = ba: ad: bd = cb: bd: cd

(ad+cd)/cb=cb/cd

we have cb=6, ad=5 and seek x=cd.

we reject the negative root and conclude x=4

answer: 4