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?
Hi Plato, thanks for the help.
that is exactly my question...
I'll try to rephrase.
the probability tree looks like this:
"probability it is flawed given A made it" (meaning P(C|A) ), if we follow the tree from its root along its branches, is
"probability that A made it" (meaning P(A) ), again, according the tree it's
so "probability it is flawed given A made it times probability that A made it" should be
Here's how I would do it:
Assume the machines produce 1000 products
so machine A produces 100 of the products.Machine A produces 10% of the factory's products.
And machine B produces 900.Machine B produces 90% of the factory's products.
1% of 100 is 1. Machine A produces 1 flawed product.1% of machine A's products are flawed.
5% of 900 is 45. Machine B produces 45 flawed products.5% of machine B's products are flawed.
Of the 1000 products 45+ 1= 46 are flawed. The probability any one is flawed is .One product randomly selected.
what is the probability that it's flawed?