How to solve a problem in probability theory?

Question

Mathematics

There are ten red and six blue balls in an urn. Two balls are drawn at random. What is the probability that both balls are the same color?
I tried to solve it like this:
P(A+B) ∪ P(C+D), where A,B are red balls and C, D are blue balls
A = 10/16, B = 9/15 (since one ball less)
C = 6/16, D = 5/15 (since there will be one ball less)
According to the probability addition theorem, I wanted to find P(A + B), but how to find P(A ∩ B) ?
P(A+B) = P(A) + P(B) - P(AB) = 5/8 + 3/5 - P(A ∩ B
) B) + P(C+D), but how to find the intersections of P(A ∩ B) and P(C ∩ D). Multiply?
Will the result be correct if you follow this solution?

Answer 1

Pairs AB and CD are successive dependent events, P _AB = P _A *P _B/A , P _CD = P _C *P _D/C

Answer 2

most probability problems are solved by making a sentence describing the probability for example: the probability is drawn 1 blue ball out of 10 blue balls or 3 red balls and pulled out 1 blue ball out of 9 blue balls or 3 red balls or pulled out 1 red ball out of 3 red or 10 blue balls and 1 ball of two red balls or 10 blue balls we
replace "from" with "divide", "and" with "multiply", "or" with "add"
we get 1/(10+3)*1/(9+3 )+1/(3+10)*1/(2+10)
but, of course, you need to think about the priority of operations =)