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Math Help - Probability

  1. #1
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    Question Probability

    Suppose that 70% of the orders on a particular website are shipped to the person who is making the order and the remaining 30% are shipped to people other than the person placing the order. Gift wrapping is requested for 60% of the orders being shipped to other people, but for only 10% of orders shipped to the person making the order.

    A) What is the probability that a randomly selected order will be gift wrapped and sent to another person?

    B) What is the probability that a randomly selected order will be gift wrapped?

    C) Is gift wrapping independent of the destination of the gift?

    Thanks to all who respond and taking your time!
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  2. #2
    Senior Member Danneedshelp's Avatar
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    Quote Originally Posted by redschaf View Post
    Suppose that 70% of the orders on a particular website are shipped to the person who is making the order and the remaining 30% are shipped to people other than the person placing the order. Gift wrapping is requested for 60% of the orders being shipped to other people, but for only 10% of orders shipped to the person making the order.

    A) What is the probability that a randomly selected order will be gift wrapped and sent to another person?

    B) What is the probability that a randomly selected order will be gift wrapped?

    C) Is gift wrapping independent of the destination of the gift?

    Thanks to all who respond and taking your time!
    Let O be the event that an order is sent to the buyer and \hat{O} be the event that the order is sent to someone else. Similiarly, let G represent the event that a gift is wrapped and \hat{G} the event that a gift is not wrapped.

    We are given,

    P(O)=0.7, P(\hat{O})=0.7, P(G|O)=0.1, and P(G|\hat{O})=0.6.

    a) We want to find the intersection of two events; namely,

    P(G\cap\hat{O})=P(G|\hat{O})P(\hat{O})=0.18

    b) We want the total probability of selecting a wrapped gift, which is

    P(G)=P(G|O)P(O)+P(G|\hat{O})P(\hat{O})
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