Basic Probability Help (2 Questions)

Hello forum,

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

Kind Regards

Frank

Re: Basic Probability Help (2 Questions)

Quote:

Originally Posted by

**MadisonDuBerlais** Hello forum,

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!

Is that all? Then you don't have enough information to answer. You need the proportion of 2-nds that arrive the next day.

Also you are trying to find $\displaystyle \text{P(2-nd} | \text{does not arrive next day})$ not $\displaystyle \text{P(does not arrive next day} | \text{ 2-nd})$

$\displaystyle \text{P(2-nd } | \text{ does not arrive next day)}=\frac{\text{P(does not arrive next day} | \text{ 2-nd) P(2-nd)}}{\text{P(does not arrive next day)}}$

CB