My names Frank and I've just signed up! I am currently struggling with my Probability especially Bayes theorem.
My first question is to find out what the probability of a letter that does not arrive the next day is 2nd class. The data I have available too me is;
1. 70% of Mail carries 1st class stamp.
2. 90% of 1st class mail arrives at its destination the next day.
Using Bayes Theorem
P(Letter Does Not Arrive/2nd Class) = 0.10 * 0.30
P(Letter Arives * 1st Class) + P(Letter does not arrive * 1st Class) = 0.72
ANS = 0.03/0.72 = 0.041
I know the ANS is 0.632 but I just don't know how to get there!
My 2nd question is;
I've bought 2 tyres, one retread and one new, after 25000m one tyre is vald and have forgotten which one is the retread. The manufacturer of the new tyre has records saying 90% lasted 25000m and the retread supplier claims that 50% of retread tyres last 25000m.
What's the probabilty that your failed tyre is a retread?
P (Failed Tyre / Retread) 0.50
P(Failed Tyre * New) 0.10