A box contains three white balls, two black balls, and one red ball. Three balls are...

A box contains three white balls, two black balls, and one red ball. Three balls are drawn at random without replacement. Let Y1 be the number of white balls drawn, and Y2 the number of black balls drawn. Find the distribution of Z = Y1 × Y2

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Y1	Y2	Z (Y1 * Y2)	P (Z)
0	0	0	0.01
1	0	0	0.09
2	0	0	0.09
3	0	0	0.01
0	1	0	0.03
1	1	1	0.27
2	1	2	0.27
3	1	3	0.03
0	2	0	0.01
1	2	2	0.09
2	2	4	0.09
3	2	6	0.01
		SUM	1

Below is the probability distribution of Z (Y1 * Y2)

Z	P (Z)
0	0.24
1	0.27
2	0.36
3	0.03
4	0.09
6	0.01
SUM	1

milcah answered 5 months ago

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