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Math Help - Maths problems about Total probability and Bayes' Theorem

  1. #1
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    Maths problems about Total probability and Bayes' Theorem

    I encounter a Maths question that I have spent for more than two hours to try but unable to figure out how to do it. Actually I finally reached the answer but I hope someone can show me the detailed solution and its tree diagram. Please.

    The question is

    The ratio of male students to female students in different forms of a school is 4:6 and the ratio of S1-2 students, S3-4 students and S5-6 students in the school is 5:4:1. The probabilities of an S1-2 student, an S3-4 student and an S5-6 student spending more than 4 hours online per day are 30%, 25%, 10% respectively. If a randomly selected student has spent more than 4 hours online in a day, find the probability that the student is an S6 male student.



    I really don't know how to draw the tree diagram and solve the question in the Bayes' Theorem's approach

    Please help, Thank you
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  2. #2
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    Quote Originally Posted by kenny1999 View Post
    I encounter a Maths question that I have spent for more than two hours to try but unable to figure out how to do it. Actually I finally reached the answer but I hope someone can show me the detailed solution and its tree diagram. Please.

    The question is

    The ratio of male students to female students in different forms of a school is 4:6 and the ratio of S1-2 students, S3-4 students and S5-6 students in the school is 5:4:1. The probabilities of an S1-2 student, an S3-4 student and an S5-6 student spending more than 4 hours online per day are 30%, 25%, 10% respectively. If a randomly selected student has spent more than 4 hours online in a day, find the probability that the student is an S6 male student.



    I really don't know how to draw the tree diagram and solve the question in the Bayes' Theorem's approach

    Please help, Thank you
    Pr(M) = 4/10, Pr(F) = 6/10.

    Pr(S1-2) = 5/10, Pr(S3-4) = 4/10, Pr(S5-6) = 1/10.

    Assume gender and year level are independent.

    Now draw a tree diagram and use it to answer the question.
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  3. #3
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    Quote Originally Posted by mr fantastic View Post
    Pr(M) = 4/10, Pr(F) = 6/10.

    Pr(S1-2) = 5/10, Pr(S3-4) = 4/10, Pr(S5-6) = 1/10.

    Assume gender and year level are independent.

    Now draw a tree diagram and use it to answer the question.
    Actuallly I am able to draw the tree diagram but I think my diagram is a bit bizarre.
    when it comes to using Bayes' Theorem to solve the problems.


    I can't draw the diagram but my tree diagram is ( I am not sure if it is correct)

    The first branch is M and F. Then for M and F themselves, each are branched into
    three possibility S1-2 , S3-4 and S5-6. Then for each sub-branch of the student level, they are then further branched into event E and complement of E (E: student who spends more than 4 hours online a day)

    Since there are three levels of branches. I don't know how to apply Bayes' Theorem to solve the problems, most reference books only show examples of
    two branches
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