Question

please show steps, thank you

One box contains 5 red and 6 blue marbles. A second box contains 10 red and 5 blue marbles. One marble is drawn from the first box and placed into the second box. After that, 3 marbles are drawn from the second box without replacement. What is the expected number of red marbles obtained on the second draw (from the second box)?

Answer 1

let X be the number of red marbles drawn from second box:

E(X|red from 1st box) =3*11/16 =33/16 (since if we draw red from 1st , then there will be 16 marble in box 2 out of which 11 are red)

E(X|blue from 1st box) =3*10/16 =30/16 (since if we draw blue from 1st , then there will be 16 marble in box 2 out of which 10 are red)

therefore

expected number of red marbles E(X) =p(red from 1st box)*E(X|ed from 1st box) +P(blue from 1st box)*E(X|blue from 1st box)

=(5/11)*(33/16)+(6/11)*(30/16)

=345/176

=1.9602