Question

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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

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PLEASE EXPLAIN AND SHOW ALL STEPS USED TO GET TO ANSWER!
THX!
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