Question

There are three white and nine red balls in a U1 box and five white and three red balls in a U2 box. We draw one ball from the U1 box and put it into the U2 box and then draw two balls from the U2 box. The probability that we draw balls of different colors from a U2 box is equal to ??????????

Answer 1

probability that we draw balls of different colors from a U2 box

=P(red from U1)*P(different color balls from U2|red from U1)+P(white from U1)*P(different color balls from U2|white from U1)

=(9/12)*((5C1)*(4C1)/(9C2))+(3/12)*((6C1)*(3C1)/(9C2))

=(9/12)*(5*4/36)+(3/12)*(6*3/36)

=13/24