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A certain dice game can only be won if, when a player throws [#permalink]

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22 Jul 2016, 09:22

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A certain dice game can only be won if, when a player throws two fair six-sided dice, the number showing on one of the dice is a multiple of the number showing on the other. What is the probability that a player wins this game?

My approach is as follows : For first dice, with 1, there will be 6 ways, Similarly for 2 on first dice, there will be 3 ways (2,4,6) For 3, on first dice, there will be 2 ways (3,6) For 4, 5 ,6 , on first dice, 1 way for each.

The answer doesn't seem to be right. Am I missing out on any possibility? (

Re: A certain dice game can only be won if, when a player throws [#permalink]

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22 Jul 2016, 09:55

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aditi2013 wrote:

[My approach is as follows : For first dice, with 1, there will be 6 ways, Similarly for 2 on first dice, there will be 3 ways (2,4,6) For 3, on first dice, there will be 2 ways (3,6) For 4, 5 ,6 , on first dice, 1 way for each.

The answer doesn't seem to be right. Am I missing out on any possibility?

First dice with 1 --> 6 ways First dice with 2 --> 3 ways First dice with 3 --> 2 ways First dice with 4, 5 and 6 --> 1 + 1 + 1 = 3 ways Total = 14

Now the entire procedure can be repeated for second dice as well --> 14 ways

We have double counted (1,1), (2,2), (3,3), (4,4), (5,5) and (6,6) --> 6

Re: A certain dice game can only be won if, when a player throws [#permalink]

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22 Jul 2016, 11:21

Vyshak wrote:

aditi2013 wrote:

[My approach is as follows : For first dice, with 1, there will be 6 ways, Similarly for 2 on first dice, there will be 3 ways (2,4,6) For 3, on first dice, there will be 2 ways (3,6) For 4, 5 ,6 , on first dice, 1 way for each.

The answer doesn't seem to be right. Am I missing out on any possibility?

First dice with 1 --> 6 ways First dice with 2 --> 3 ways First dice with 3 --> 2 ways First dice with 4, 5 and 6 --> 1 + 1 + 1 = 3 ways Total = 14

Now the entire procedure can be repeated for second dice as well --> 14 ways

We have double counted (1,1), (2,2), (3,3), (4,4), (5,5) and (6,6) --> 6

Re: A certain dice game can only be won if, when a player throws [#permalink]

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23 Jul 2017, 12:15

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Or simply just list what the question asks, i.e. pairs in which one is the factor of another: 1--pairs with (1,2,3,4,5,6) 2--pairs with (1,2,4,6) 3--pairs with (1,3,6) 4--pairs with (1,2,4) 5--pairs with (1,5) 6--pairs with (1,2,3,6)