1 white 1 yellow, 2 white, 2 yellow
The probability of bag A getting 1 white 1 yellow 2 white 2 yellow is
P( 1 white 1 yellow) = C3 (1) * C2 (1)/C5 (2) = 3/5.
P(2 white) =C3(2)/C5(2)=3/ 10.
P(2 yellow) = C2 (2)/C5 (2) =110
The probability of bag B getting 1 white 1 yellow 2 white 2 yellow is
P( 1 white 1 yellow) = C5 (1) * C3 (1)/c8 (2) =15/28.
P(2 white) =C5(2)/C8(2)=5/ 14
P(2 yellow) =C3(2)/C8(2)=3/28
The absolute value of the difference between the number of yellow balls and the number of white balls is x: 0, 2, 4.
p(x = 0)= 3/5 * 15/28+3/ 10 * 3/28+ 1/ 10 * 5/ 14 = 109/208
P(x=2)= 138/280
P(x=4)=33/280
Probability distribution of x
X 0 2 4
p 109/280 138/280 33/280
Expected value of mathematics
EX = 0x 109/280+2x 138/280+4x 33/280 = 5 1/35