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Math Help - probability gambling

  1. #1
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    probability gambling

    . In the XVII century Lord de Mere, a vivid gambler, asked Pascal, one of the great mathematicians of his time: If a player rolls a die 4 times what should I bet on: a) he rolls at least one 6; or b) he does not roll a 6 at all? What would you bet on?
    so for this question I would say a. because it would a 4 in 6 chance or a 0.667 chance
    anybody have another way of showing this because I think i might me wrong
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  2. #2
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    Hello, mr.toronto!

    If a player rolls a die 4 times, what should I bet on:
    a) he rolls at least one 6, or
    b) he does not roll a 6 at all?
    What would you bet on?
    Your reasoning is incorrect . . .

    One any roll, P(6) \:=\:\frac{1}{6},\;P(\text{other}) \:=\:\frac{5}{6}

    b) The probability that he rolls no 6's is: . \left(\frac{5}{6}\right)^4 \:=\:\frac{625}{1296} \:\approx\:0.482

    a) Hence: . P(\text{at least one 6}) \:=\:1 - 0.482 \:=\:0.518

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  3. #3
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    k so he should bet on at least one six since there is a 0.518% he will roll at least one six
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  4. #4
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    Quote Originally Posted by mr.toronto View Post
    . In the XVII century Lord de Mere, a vivid gambler, asked Pascal, one of the great mathematicians of his time: If a player rolls a die 4 times what should I bet on: a) he rolls at least one 6; or b) he does not roll a 6 at all? What would you bet on?
    so for this question I would say a. because it would a 4 in 6 chance or a 0.667 chance
    anybody have another way of showing this because I think i might me wrong
    Work from the case where no sixs are rolled.

    Probability of not rolling a six on a single roll is 5/6

    Probability of this occuring on all four rolls (5/6)^4 ~= 0.4823

    Probability of rolling at least one six = 1- prob of rolling no sixes = 1-(5/6)^4 ~= 0.5177

    RonL
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  5. #5
    Grand Panjandrum
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    Quote Originally Posted by mr.toronto View Post
    k so he should bet on at least one six since there is a 0.518% he will roll at least one six
    If the bet is being offered at evens, otherwise it depends on the odds he is being offered.

    RonL
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