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Math Help - another spinner prob

  1. #1
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    another spinner prob

    A circular spinner has 8 equally spaced spots; there are 3 blue, 2 green, 2 yellow and 1 red space. Let events A and B be defined as follows:
    A = {outcomes with a blue on the first spin}
    B = {outcomes with yellow on a spin}

    Find:
    a.) probability (A)

    b.) probability (B)

    c.)probability (A union B)

    I have questions about all 3:
    a.) would this just be 3/8, or do i need to factor in the second spin

    b.) would this be 1/64 = 1/8 * 1/8

    c.) what exactly is this part asking? prob(blue followed by a yellow)??? and if so would this just be 3/8 * 1/8 = 3/64?
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  2. #2
    MHF Contributor matheagle's Avatar
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    It looks like you are spinning the wheel twice.
    But who knows.
    A is 3/8 no matter how many spins
    Do you want exactly two or at least one yellow in B?
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  3. #3
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    oops, that's my bad...the spinner is spun twice and its b = {outcomes with yellow on a spin}, so i am assuming that means at least one yellow

    sorry
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  4. #4
    MHF Contributor matheagle's Avatar
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    Quote Originally Posted by ihavvaquestion View Post
    oops, that's my bad...the spinner is spun twice and its b = {outcomes with yellow on a spin}, so i am assuming that means at least one yellow

    sorry
    Instead of looking at the event of at least one yellow.
    Use the complement, no yellow...1-(3/4)(3/4).
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  5. #5
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    ok thanks that makes sense
    so the probability of yellow on a spin would look like this:

    n(s) = 8*8 =64
    n(no yellow) = 6*6 =36
    n(a yellow) = 28

    prob(no yellow) = 36/64 = 9/16
    prob(outcomes of yellow on a spin) = 28/64 = 7/16


    then for the last part...what does a union b mean. does that mean a then b?
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  6. #6
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    Union means both A and B occur. With the events in this example, this basically means the event that you get a blue first, then a yellow, so in this case it does mean A then B, but this wouldn't always be the case. I believe the probability you calculated is correct.
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  7. #7
    MHF Contributor matheagle's Avatar
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    Quote Originally Posted by statsnoob View Post
    Union means both A and B occur. With the events in this example, this basically means the event that you get a blue first, then a yellow, so in this case it does mean A then B, but this wouldn't always be the case. I believe the probability you calculated is correct.

    sorry
    union is an or
    intersection is an and, meaning BOTH sets must occur.
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  8. #8
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    so A u B means A or B, or A and B?

    if so does this mean (3/8) + (7/16) + (3/8)*(7/16)
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  9. #9
    MHF Contributor matheagle's Avatar
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    P(A\cup B)=P(A)+P(B)-P(AB)

    where AB is the intersection of A and B.

    The event AB means BOTH must occur

    While A\cup B means at least one must occur, maybe both.
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  10. #10
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    so would 3/8 + 7/16 - P(AB) be correct?

    and for P(AB) would I just multiply (3/8)(1/4)? that being 3/8 prob of blue on 1st spin and (1/4) prob of yellow on the second spin

    thanks for your help
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  11. #11
    MHF Contributor matheagle's Avatar
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    Quote Originally Posted by ihavvaquestion View Post
    so would 3/8 + 7/16 - P(AB) be correct?

    and for P(AB) would I just multiply (3/8)(1/4)? that being 3/8 prob of blue on 1st spin and (1/4) prob of yellow on the second spin

    thanks for your help
    P(AB)=P(A)(B) ONLY if the sets are independent, which I doubt.

    That is one of the many equivalent definitions of independence.
    Here you need to figure out what the set AB entails and then compute its probability.

    Or figure out the set A\cup B and compute its probability.
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