All those good with statistics

my take on the second one.

for X squared to be > a, X must be either less than -s or greater than s (standard deviation). In a normal distribution, that is approx 32% of the data (don't have my tables or calc at home, but i'm sure that you can find it easily).

too tired and lazy to take on a tree diagram for the first.

1) The answer the question is looking for is 5/9, which is (1/5)*(.10) divided by (1/5)*(.10) + (4/5)*(.02). However, this is not really right but I don't wanna get into it...

For the second one, if X is random normal then X squared is Chi squared. Use the Chi squared distribution to figure out the probability. I'll have to work on the first one, but it is Bayesian in nature, which I hate.

Oh wait. I misread the question...back in a sec with answer.

Let x = (1/5)(30)(0.9)^29(0.1)

Let y = (4/5)(0.98)^29(0.02)

x = the probability that the sample comes from company x and there is one defective sample

y = the probability that the sample comes from company y and there is one defective sample

the probability that the sample is from company x, given that there is one defective sample is x/(x+y)

Yeah that's what I got. So like 9.6% chance.

Thankfully Kartelite is working on number one. For number two, if X is normal with variance a, then X squared/a is chi squared with one degree of freedom (I think). Should be easy then to figure out the probability of a chi square with one degree of freedom being greater than 1. I'm guessing around 0.5.

Both of the answers on the second question are correct, but the first way is much more direct and intuitive (in my opinion). The answer would be around 32%.

probability guy wrote:

Let x = (1/5)(30)(0.9)^29(0.1)

Let y = (4/5)(0.98)^29(0.02)

x = the probability that the sample comes from company x and there is one defective sample

y = the probability that the sample comes from company y and there is one defective sample

the probability that the sample is from company x, given that there is one defective sample is x/(x+y)

I forgot a factor of 30 in y. So,

y = (4/5)(30)(0.98)^29(0.02)

Wouldn't the answer to number 1 be 0.2. They selected one shipment and 1/5th of the shipmates come from company X.

Keep it simple wrote:

Wouldn't the answer to number 1 be 0.2. They selected one shipment and 1/5th of the shipmates come from company X.

Not so! If we only said "a sample was chosen, what is the probability that it came from company X," then your answer would be correct. But since we know that the sample of 30 had one defect, the probability changes.

Here is a simpler example to illustrate the point. Suppose there are 100 boys and 100 girls. 99 boys are wearing white shirts, 1 boy is earing a red shirt, and all of the girls are wearing a red shirt. A person is picked at random, and all we know is that the person is wearing a red shirt. What is the probability that the person is a boy? Not very likely, since 100 out of every 101 times it will be a girl. To be exact, the probability that it is a girl will be 100/101, and for a boy it will be 1/101.