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Math Help - One Spinner 3 Colors

  1. #1
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    Smile One Spinner 3 Colors

    Three spinners are given:

    Spinner 1 has 4 sections divided by the numbers 1, 2, 3 and 4.

    Spinner 2 has three sections divided by the following colors: Red, Green and Yellow.

    Spinner 3 has 2 sections divided by the words Forward and Backward.

    (1) Spin spinner 3, then spinner 2. What is the probability of getting Forward, followed by Yellow or Green?

    (2) Spin spinner 2, then spinner 1 and then spinner 3. What is the probablity of getting Yellow, followed by a 2 or a 4, followed by Backward?

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  2. #2
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    Assuming each of the areas on each spinner are of equal size (you didn't say that), all the outcomes are equally likely. The first spinner has 4 equally likely areas so the probability of any one of them is 1/4. The second spinner has 3 equally likely areas so the probability of any one of them is 1/3. The third spinner has two equally likely areas so the probability of any one of them is 1/2.

    If A and B are "mutually exclusive" (as are different areas on each spinner- the needle cannot point to two different areas) then the probability of "A or B" is the probability of A plus the probability of B.

    If A and B are "independent" (as are the results of different spinners- the result of one spin does not affect the spin of another) then the probability of "A and B" is the product of the probability of A and the probability of B.

    The probability of "forward" is 1/2 and the probability of "yellow or green" is 1/3+ 1/3= 2/3. The probability of getting "forward" and "yellow or green" is (1/2)(2/3)= 1/3.


    The probability of getting "yellow" is 1/3, the probability of getting "2 or 4" is 1/4+ 1/4= 1/2, and the probability of getting "backward" is 1/2. The probability of getting "yellow" and "2 or 4" and "backward" is (1/3)(1/2)(1/2)= 1/12.
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  3. #3
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    Thanks....

    Quote Originally Posted by HallsofIvy View Post
    Assuming each of the areas on each spinner are of equal size (you didn't say that), all the outcomes are equally likely. The first spinner has 4 equally likely areas so the probability of any one of them is 1/4. The second spinner has 3 equally likely areas so the probability of any one of them is 1/3. The third spinner has two equally likely areas so the probability of any one of them is 1/2.

    If A and B are "mutually exclusive" (as are different areas on each spinner- the needle cannot point to two different areas) then the probability of "A or B" is the probability of A plus the probability of B.

    If A and B are "independent" (as are the results of different spinners- the result of one spin does not affect the spin of another) then the probability of "A and B" is the product of the probability of A and the probability of B.

    The probability of "forward" is 1/2 and the probability of "yellow or green" is 1/3+ 1/3= 2/3. The probability of getting "forward" and "yellow or green" is (1/2)(2/3)= 1/3.


    The probability of getting "yellow" is 1/3, the probability of getting "2 or 4" is 1/4+ 1/4= 1/2, and the probability of getting "backward" is 1/2. The probability of getting "yellow" and "2 or 4" and "backward" is (1/3)(1/2)(1/2)= 1/12.
    I thank you for your detailed reply.
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