Question by Sarah: Help with probability question?
The Squeaky Clean company makes bar soap in two production facilities: Pennsylvania and Missouri. Squeaky Clean’s Missouri facility accounts for 60% of the bars produced with the remaining 40% produced in Pennsylvania. Squeaky Clean makes the same soap in both facilities and ships it to a single warehouse for distribution. Bars of soap are then shipped from the warehouse to retail outlets (grocery stores, drug stores, convenience stores, etc.) so the retailers do not know the production facility of the soap they have. Therefore, assume that each bar of soap at a store has a 60% of being produced in Missouri and the production location of one bar of soap is independent of other bars of soap. The bars of soap are imprinted with the Squeaky Clean company logo at the production facility. Due to the nature of the process, not all bars get imprinted with the company logo.
At the Pennsylvania facility 10% of the soap does not receive the company logo and 5% of the soap produced in Missouri does not get the logo.
a) What proportion of all soap bars produced have the Squeaky Clean logo? Hint: condition and use Total Probability Rule.
b) You just purchased a bar of soap and notice that it does not have the Squeaky Clean logo. What is the probability this bar was produced in the Missouri facility? Hint: Bayes
Answer by Sushi
Know better? Leave your own answer in the comments!