my approach was like this ,
Assuming 𝑛 ∈ ℕ∗,two numbers are drawn randomly. Lets call the first one 𝑥 and the second 𝑦. Furthermore we learn that both are drawn from the uniform distribution on {0,1}. (Actually the distribution is not given, but I chose a simple one to not complicate matters). Because the two events are supposed to be independent (which I also assume),
we can draw all possibly combinations as a pair of numbers (𝑥,𝑦) that is (0,1) & (1,0),
We need to establish the probability the number 5x+y is divisible by 3.
case1:
when (𝑥,𝑦) = (0,1) :
we get 5x+y = 1
1 is not divisible by 3.
case2:
when (𝑥,𝑦) = (1,0) :
we get 5x+y = 5
5 is not divisible by 3.
so the probability that 5x+y within interval {0,1} is divisible by 3 is zero.
I am definitely not convinced by my approach . kindly suggest.
Best Answer
You've got the right idea, but you're missing half the cases. Since $x$ and $y$ are independent, they can take the same value; we're sampling with replacement, if you like. As well as $(0,1)$ and $(1,0)$, $(x,y)$ can also be equal to $(0,0)$ or $(1,1)$. Add those two cases, and you should get the answer you're looking for.