Two machines, A and B, operate in some factory.

Machine A produces 10% of the factory's products.

Machine B produces 90% of the factory's products.

1% of machine A's products are flawed.

5% of machine B's products are flawed.

One product randomly selected.

what is the probability that it's flawed?

So, this is what I did:

let

let

let

Now, according to the law of total probability, we'll get that:

but the answer is:

Why were and omitted?