Thread: probability

a six faced die is so biased that it is twice as likely to show an even number as an odd number when thrown. it is thrown twice. what is the probability that the sum of 2 numbers thrown is even

Ok, let's start like this

even + even = ...
odd + even = ...
even + odd = ...
odd + odd = ...

Condition on the first throw.

P(sum is even) = P(sum is even|first throw is even)*P(first throw is even) + P(sum is even|first throw is odd)*P(first throw is odd) = (2/3)*(2/3) + (1/3)*(1/3) = 5/9