TITLE: I got the answer as 7/16 , can anyone confirm it?
QUESTION [9 upvotes]: Box A contains 5 red and 3 white marbles Box b contains 2 red and 6 white marbles if a marble is drawn from each box, what is the prob that they are of same colour.

My solution:
RR  or WW
= (5/8)(2/8)  + (3/8)(6/8)
= 10/64 + 18/64
= 28/64
= 7/16
My teacher's solution:
Let E1 be the event that marble is from Box A and is Red:
P(E1)=(1/2)(5/8)= 5/16
Let E2 be the event that marble is from Box B and is Red:
P(E2)=(1/2)(2/8)= 1/8
Let E3 be the event that marble is from Box B and is White:
P(E3)=(1/2)(3/8)= 3/16
Let E4 be the event that marble is from Box B and is White:
P(E4)=(1/2)(6/8)= 3/8
Required Probability= P(E1nE2)+P(E3nE4)= (5/16)(1/8)+(3/16)(3/8)= 7/64
can anyone confirm which one is correct?

REPLY [2 votes]: Let $E_1$ be the event that marble is from Box A and is Red: $P(E_1)=(1/2)(5/8)= 5/16$

There is no need to multiply by $1/2$, the probability for selecting the box, as you are not randomly selecting boxes.
You are drawing a marble from each box, so that is certainly what will happen.
$E_1$ should be the event that the marble drawn from box A is red: $\mathsf P(E_1)=5/8$.
This is what you had calculated, and likewise  for the others.
So your calculation was correct.$$\dfrac{5}{8}\cdot\dfrac 28 + \dfrac 38\cdot\dfrac 68 = \dfrac{7}{16}$$