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Math Help - Theoretical probability

  1. #1
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    Theoretical probability

    John is collecting a set of 4 Native Birds cards, from Oatie Flakes cereal packets.
    The manufacturers of Oatie Flakes found that some of their machines malfunctioned and 20% of the packets of cereal contain 2 Native Birds cards instead of 1 card.

    In John’s class there are 22 students (including John) trying to collect the Native Bird card set.

    1. After a while 20 of the 22 students in John’s class have only one card left to get for the complete set.
    a) Use theoretical probability to predict how many of these 20 students will complete their set with the next packet of Oatie Flakes.
    b)Use theoretical probability to predict how many of these 20 students will complete their set given that the next packet is a 2-card packet of Oatie Flakes.

    Can someone please show me how to do this?
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  2. #2
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    Quote Originally Posted by Paulo1913 View Post
    John is collecting a set of 4 Native Birds cards, from Oatie Flakes cereal packets.
    The manufacturers of Oatie Flakes found that some of their machines malfunctioned and 20% of the packets of cereal contain 2 Native Birds cards instead of 1 card.

    In John’s class there are 22 students (including John) trying to collect the Native Bird card set.

    1. After a while 20 of the 22 students in John’s class have only one card left to get for the complete set.
    a) Use theoretical probability to predict how many of these 20 students will complete their set with the next packet of Oatie Flakes.
    b)Use theoretical probability to predict how many of these 20 students will complete their set given that the next packet is a 2-card packet of Oatie Flakes.

    Can someone please show me how to do this?
    Draw a tree diagram. The first branches are getting a two card pack or not. The second branches are a particular card or not.

    (a) Note: In a one card pack, the probability of a particular card is 1/4. In a two card pack the probability of a particular card is 2/4.

    So the total probability of getting a particular card is (1/5)(2/4) + (4/5)(1/4) = 6/20 = 3/10.

    So now it's a binomial distribution problem ...... X is the random variable number of students who get the card they need (and hence complete their set), n = 20, p = 3/10.

    E(X) = np = .....
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  3. #3
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    Quote Originally Posted by Paulo1913 View Post
    John is collecting a set of 4 Native Birds cards, from Oatie Flakes cereal packets.
    The manufacturers of Oatie Flakes found that some of their machines malfunctioned and 20% of the packets of cereal contain 2 Native Birds cards instead of 1 card.

    In John’s class there are 22 students (including John) trying to collect the Native Bird card set.

    1. After a while 20 of the 22 students in John’s class have only one card left to get for the complete set.
    a) Use theoretical probability to predict how many of these 20 students will complete their set with the next packet of Oatie Flakes.
    b)Use theoretical probability to predict how many of these 20 students will complete their set given that the next packet is a 2-card packet of Oatie Flakes.

    Can someone please show me how to do this?
    (b) Still binomial. n = 20, p = 2/4 = 1/2. E(X) = ......
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  4. #4
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    So for A E(x)=6 students and B E(x)= 10 students?
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  5. #5
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    Quote Originally Posted by Paulo1913 View Post
    So for A E(x)=6 students and B E(x)= 10 students?
    Yes.
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  6. #6
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    Simulation Help!!!!!!!!!!!!!!!!!!!!!!!

    Quote Originally Posted by mr fantastic View Post
    (b) Still binomial. n = 20, p = 2/4 = 1/2. E(X) = ......
    Hi Mr Fantastic

    Thanks for getting the theoratical probability of this problem but still stuck how to use calculator to actaually simulate the probleb of getting 4 different birds.
    Could you please, help me more?

    Thanks
    Parveen
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  7. #7
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    Post Still need help!!!!!!!

    hi there

    Thanks for quick reply and it hepled me with theoretical prob.and bit of simulating using Calculator
    but how we know out of 4 boxes if he get 1 box malfunctioned, will this box contains the same kind of birds or different birds so that he is able to collect all 4 bird cards?

    Could you help me more to clarify this please by showing working a bit?

    Regards
    Parveen
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