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Thread: Discrete Math: E_1 is scores odd, different; E_2 is scores sum to 8; independent?

  1. #1
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    Question Discrete Math: E_1 is scores odd, different; E_2 is scores sum to 8; independent?

    5. Two different colored fair dice are thrown. Let E1 be the event that the scores are both odd but different, and let E2 be the event that the sum of the scores is 8. Are the events E1 and E2 independent? (Note: You must justify your answer!)

    How would i go about justifying?

    Is my solution ok?

    Even value in 1 to 6 are 2,4,6

    Number of even value in 1 to 6 are 3

    E1 = (3*2)/36 = 1/6

    Odd value in 1 to 6 are 1,3,5

    Number of odd value in 1 to 6 are 3

    E2 = (3*2)/36 = 1/6

    Yes, E1 and E2 are equal.
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    Last edited by stapel; 03-07-2018 at 06:08 PM. Reason: Typing out the text in the graphics; creating useful subject line.

  2. #2
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    Quote Originally Posted by sita View Post
    5. Two different colored fair dice are thrown. Let E1 be the event that the scores are both odd but different, and let E2 be the event that the sum of the scores is 8. Are the events E1 and E2 independent? (Note: You must justify your answer!)

    How would i go about justifying?

    Is my solution ok?

    Even value in 1 to 6 are 2,4,6

    Number of even value in 1 to 6 are 3

    E1 = (3*2)/36 = 1/6

    Odd value in 1 to 6 are 1,3,5

    Number of odd value in 1 to 6 are 3

    E2 = (3*2)/36 = 1/6

    Yes, E1 and E2 are equal.
    Your attempted solution does not seem to be even addressing the problem given. They give you a helpful clue by suggesting that you think about dice of different colors.

    How many any of the 36 possible rolls will result in an odd number on the red die?

    Half of them, right, so 18?

    How many of the 36 possible rolls will result in an odd number on the green die?

    Again, half of them so 18.

    But 18 + 18 = 36 so does this mean none of the possible rolls give an even number on either die.

    I suggest that that you START by building a little table of the 36 possibilities and CONTINUE by counting how many possibilities give event 1 and how many give you event 2. Only then can you begin to think about independence. By the way, what is the definition of independence?
    Last edited by stapel; 03-07-2018 at 06:09 PM. Reason: Copying typed-out graphical content into reply.

  3. #3
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    E2 is 5/6. Rethink this.

    Why do we need to know if the two probabilities are equal? What is the Test for Independence? There is a formula for that.
    "Unique Answers Don't Care How You Find Them." - Many may have said it, but I hear it most from me.

  4. #4
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    Quote Originally Posted by sita View Post
    5. Two different colored fair dice are thrown. Let E1 be the event that the scores are both odd but different, and let E2 be the event that the sum of the scores is 8. Are the events E1 and E2 independent? (Note: You must justify your answer!)

    How would i go about justifying?

    Is my solution ok?

    Even value in 1 to 6 are 2,4,6

    Number of even value in 1 to 6 are 3

    E1 = (3*2)/36 = 1/6

    Odd value in 1 to 6 are 1,3,5

    Number of odd value in 1 to 6 are 3

    E2 = (3*2)/36 = 1/6

    Yes, E1 and E2 are equal.
    E1 and for E2 as stated in the problems are events NOT numbers. That is E1 and for E2 are NOT probabilities. You can compute the probabilities of events. For example, you can compute the probability of E1, denoted by P(E1), but E1 and for E2 are NOT probabilities. Notation is important.
    Last edited by stapel; 03-07-2018 at 06:09 PM. Reason: Copying typed-out graphical content into reply.
    A mathematician is a blind man in a dark room looking for a black cat which isnít there. - Charles R. Darwin

  5. #5
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    Quote Originally Posted by Jomo View Post
    E1 and for E2 as stated in the problems are events NOT numbers. That is E1 and for E2 are NOT probabilities. You can compute the probabilities of events. For example, you can compute the probability of E1, denoted by P(E1), but E1 and for E2 are NOT probabilities. Notation is important.
    Can you write out all the events in E1?
    A mathematician is a blind man in a dark room looking for a black cat which isnít there. - Charles R. Darwin

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