Having some trouble with this homework assignment; not looking for a direct answer but some guidance.
I have a tortilla making machine for which I need to replace a part in order to get it working. I evaluate the efficiency of the tortilla maker by the proportion of failures it produces (the number of square tortillas). It can only ever produce round or square tortillas.
I have a box of replacement parts that I need to choose one from and place into my tortilla making machine. These parts come in two types: Type 1 has a failure rate of .4, and Type 2 has a failure rate of .75. I also know that, in that box, 30% of the replacement parts are of type 1.
I choose a replacement part from the box at random, a place it into the machine and I use the machine to make 30 tortillas; of these, I find that 16 of the tortillas it created are square (failures).
Question: What is the probability that I picked a Type 1 part?
Answer so far:
I think this problem involves binomial distributions and conditional probability.
The first thing I did was calculate the probability that a Type 1 and Type 2 part could produce a 16/30 outcome. To do this I used binomial distributions and produced these results:
- Type 1 : p = .0489 (That is, a Type 1 part is going to produced 16/30 failed tortillas just shy of 5% of the time)
- Type 2 : p = .0054
My trouble is how exactly to incorporate the information regarding the underlying distribution in the box. Would I use conditional probability here? That is: Calculate:
P(I picked a Type 1 part Given that it produced 16/30 failures)?
Would I need to calculate a general probability of producing 16/30 failures, independent of part Type?
Looking for Guidance! Thanks!