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Math Help - Dice Prroblem

  1. #1
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    Dice Prroblem

    A regular die is thrown 4 times. Find the probability that:

    a.) a 5 will come up all 4 times.




    b.) if a 6 is thrown on the first throw, a 6 will also be thrown on the last throw

    To a i think its 4C4*(1/6)^4 *(5/6)^0
    and to be i think its 4C1*(1/6)^1*(5/6)^3



    So umm..help please?
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  2. #2
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    Quote Originally Posted by lax600 View Post
    A regular die is thrown 4 times. Find the probability that:

    a.) a 5 will come up all 4 times.




    b.) if a 6 is thrown on the first throw, a 6 will also be thrown on the last throw

    To a i think its 4C4*(1/6)^4 *(5/6)^0 Mr F says: Correct.

    and to be i think its 4C1*(1/6)^1*(5/6)^3 Mr F says: Incorrect. The answer is 1/6. See below.



    So umm..help please?
    All throws are independent. The fact you got a 6 on the first throw has absolutely no influence on what happens on the last throw.

    Here's something to consider ...... you throw three times and get a 6 on the first throw. You put the die in your pocket. A week later you do your fourth throw. The probability of getting a 6 is obviously 1/6 .....
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    uhh i dont think i understand
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    Quote Originally Posted by lax600 View Post
    uhh i dont think i understand
    What don't you understand?

    The last throw is independent of what's happened in all previous throws, including the first throw. That means that the probability of rolling a 6 on the last throw, regardless of what the previous rolls were, is 1/6.

    If I toss a coin and it comes up heads, what's the probability that it'll come up heads on the second toss? I hope you say 1/2 .... What's the probability it'll come up heads on the fourth toss? Again, I hope you say 1/2 .....

    Do you understand what it means for events to be independent?
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  5. #5
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    ok so the first roll is 1/6 and the last roll is also 1/6, what about the second and third throws?

    and is it just simply 1/6 or is there more to it?
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  6. #6
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    Quote Originally Posted by lax600 View Post
    ok so the first roll is 1/6 and the last roll is also 1/6, what about the second and third throws?

    and is it just simply 1/6 or is there more to it?
    Every roll is independent. Do you understand what that means?
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