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    Hi, I have been stuck with this example for quite a while now. The question is as follows:


    A customer entering a bicycle store will buy a new bike with a probability of 10% and will buy bicycle accessories with a probability of 65%. With a probability of 30% a customer will not purchase anything.

    (a) Find the probability that a customer will buy both a new bike and bicycle accessories.
    and (b) Find the probability that a customer will only buy a bike.

    I have done similar questions before however with this question I don't quite understand what to do with.

    For part (a) I did the following:

    A = buy a bike. P(A) = 0.1
    B = buy bike accessories. P(B) = 0.65

    Then I tried to use the formula:
    P(A u B) = P(A) + P(B) - P(A n B) but I don't know how I would find P(A n B).

    In the end I got a value of 0.685 but don't think its correct.
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    You can think of A \cap B as being where A and B overlap.

    Notice that the probabilities sum to more than 100%; and also notice that a customer can't both buy nothing and buy something. A customer buys at least something with probability P(A \cup B), and buys both bike accessories and a bike with probability P(A \cap B). The first of these facts means that we must have P(A \cup B) = 1 - P(\text{buys nothing}).
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    (Original post by nuodai)
    You can think of A \cap B as being where A and B overlap.

    Notice that the probabilities sum to more than 100%; and also notice that a customer can't both buy nothing and buy something. A customer buys at least something with probability P(A \cup B), and buys both bike accessories and a bike with probability P(A \cap B). The first of these facts means that we must have P(A \cup B) = 1 - P(\text{buys nothing}).

    This is my answer to part (a)

    P(A u B) = 1 - P( not buy anything)
    = 1- 0.3
    = 0.7

    P(A u B) = P(A) + P(B) - P(A n B)
    P(A n B) = 0.1 + 0.65 - 0.7
    = 0.05

    Would the answer to part (b) also be 0.05?

    Thank you.
    • Study Helper
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    (Original post by axa121)
    This is my answer to part (a)
    = 0.05

    Would the answer to part (b) also be 0.05?
    Yes, and yes.
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    Ok many thanks.
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    a) 0.65 x 0.1 = 0.065 = 6.5%

    b) 100- (65+10+30) = 5
    5 (used bike?) + 10 (new bike) = 15%

    I'm not sure if that is what the question wants though
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    (Original post by sinadoom)
    a) 0.65 x 0.1 = 0.065 = 6.5%

    b) 100- (65+10+30) = 5
    5 (used bike?) + 10 (new bike) = 15%

    I'm not sure if that is what the question wants though
    Both those answers are wrong, and without any explanation it just looks like you've taken some of the numbers there and added/multiplied them together at random And where is there any mention of used bikes?
 
 
 
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