Math

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A die is rolled twice. What is the probability that the sum of the rolls is less than 4 given that one of the rolls is a 1?

The answer is 3/11. Could someone tell me how to get this. Thanks?

  • Math -

    The rolls are independent. If you have already obtained a 1, you are asking for the probability of getting either a 1 or 2 to add to "less than 4."

    1/6 + 1/6 = 2/6 = 1/3

    With 6 possibilities for any roll of a die, there is no way of getting a denominator of 11.

    http://www.members.cox.net/dagershaw/lol/Odds.html

  • Math -

    Possibilities with rolling 3 on ONE of the rolls:
    First roll: 1,1 | 1,2 | 1,3 | 1,4 | 1,5 | 1,6
    Second roll: 1,1 | 2,1 | 3,1 | 4,1 | 5,1 | 6,1

    Eliminate 1,1 from second roll because it is the same as in the first, therefore there are 11 possibilities with 1 as either the first or second roll.

    Find the rolls that are less than 4.
    (1,1) (1,2) (2,1). 3 rolls are less than 4.

    Therefore P(x < 4) = 3 / 11.

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