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Math Help - Basic Probability Help (2 Questions)

  1. #1
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    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
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  2. #2
    Grand Panjandrum
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    Re: Basic Probability Help (2 Questions)

    Quote Originally Posted by MadisonDuBerlais View Post
    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 \text{P(2-nd} | \text{does not arrive next day}) not \text{P(does not arrive next day} | \text{ 2-nd})

    \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
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