Probability that a battery is faulty from two shops

[matt222]

Homework Statement

Two shops where

75% of battery come from shop 1
25% of battery come from shop 2 also
99% from shop 1 ok
90% from shop 2 ok
1- what is the probability that a particular battery is faulty
2- given that its faulty, what is the probability it came from shop 1

Homework Equations

The Attempt at a Solution

for question 1 it is 0.01+0.1=0.11%
for the second one is 0.01
is it true

 

[statdad]

Not true - you need an approach that takes into account the percentages of batteries that come from the two shops. Think about that, and show a little more work. (Hint: have you discussed tree diagrams? Bayes' Theorem?)

 

[HallsofIvy]

The simplest thing to do is to imagine you have 10000 batteries (chosen just to avoid fractional batteries). 75% of 10000= 7500 are from shop 1 and 25% of 10000= 2500 are from shop 2. 1% of the batteries from shop 1 are faulty so you have 1% of 7500= 75 faulty batteries from shop 1 and 10% of the batteries from shop 2 are faulty so you have 10% of 2500= 250 faulty batteries from shop 2.

You have a total of 75+ 250= 325 faulty batteries out of 10000. What percentage is that?

You have a total of 325 faulty batteries and 75 of them are from shop 1. What percentage is that?

 

[matt222]

for the first one going to be 3.25% and for the second one is 0.75%, is it right