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Math Help - Basic Probabilty

  1. #1
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    Smile Basic Probabilty

    Of 500 students , 200 participating in math activity , 250 participating in science activity and 50 participated in both activities , Find that a randomly selected student.
    a) Will be a participant in at least one of the two activities.
    b) Will not be a participant in either activity.
    c) Will be a participant in exactly one activity.

    My answer :
    a) 0.8
    b) 0.3
    c) 0.5

    Is my answer correct?
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  2. #2
    MHF Contributor Unknown008's Avatar
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    For the first one, yes.

    But for the other two... can I ask you how you got those answers?
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  3. #3
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    First , Thank you
    Second , here is it
    P(M)=0.4
    P(S)=0.5
    P(M AND S)=0.1

    a)
    P(M OR S)= P(M)+P(S)-P(M AND S)

    b)
    P(M')=0.6
    P(S')=0.5
    P(M' AND S') = P(M') . P(S')

    c)
    P(S' AND M) OR P(S AND M') = P(M) . P(S') +[P(M') . P(S)]
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  4. #4
    MHF Contributor Unknown008's Avatar
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    b). Ah, there is your mistake. The probability that the student will not be a participant in either activities is:

    P(M \cup S)' = 1 - P(M \cup S) = 1 - 0.8 = 0.2

    Drawing a Venn Diagram might be easier to follow.

    c). Here also, a Venn Diagram would show you the right answer. You didn't remove the set M \cap S

    Let me show you the Venn Diagram:



    You will immediately see that those who will not be participant in either activities is 100 over 500.

    And for c), it becomes (150 + 200)/500 = 0.7
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  5. #5
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    Thank a lot
    But I'm still confused for part c
    who will not be participant in either activities is 100 over 500.
    From where you got 100 student will not be participant??
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  6. #6
    MHF Contributor Unknown008's Avatar
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    They are those which aren't in any of the sets.

    You know that 50 students perform both, hence the 50 in the intersection of the sets.

    You know a total of 200 perform in math, hence, 150 performed only math.
    You know a total of 250 perform in science, hence, 200 performed only science.

    Total up to now is 150 + 50 + 200 = 400

    which means, 100 of them don't do either.

    The probability then becomes obvious.
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  7. #7
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    aha got it thank you
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