Probability Problem

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nehatandon: Junior | Next Rank: 30 Posts; Posts: 13; Joined: Fri Jan 07, 2011 9:17 pm

by nehatandon » Fri Jan 07, 2011 9:23 pm

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?
(A)11/18
(B)11/36
(C)1/4
(D)2/9
(E)7/36

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Source: Beat The GMAT — Problem Solving | Fri Jan 07, 2011 9:23 pm

anshumishra: Legendary Member; Posts: 543; Joined: Tue Jun 15, 2010 7:01 pmFollowed by: 3 members; Thanked: 147 times

by anshumishra » Fri Jan 07, 2011 9:44 pm

nehatandon wrote: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?
(A)11/18
(B)11/36
(C)1/4
(D)2/9
(E)7/36

Here are the ways in which a player can win

1st dice------------ 2nd dice
1------------ 1,2,3,4,5,6
2------------ 1,2,4,6
3------------ 1,3,6
4------------ 1,2,4
5------------ 1,5
6------------ 1,2,3,6

Favorable no. of outcomes = 6+4+3+3+2+4 = 22
Total no. of outcomes = 6*6 = 36

So, required probability = 22/36 = 11/18 A

Thanks
Anshu

(Every mistake is a lesson learned )

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Ramit88: Senior | Next Rank: 100 Posts; Posts: 67; Joined: Fri Nov 26, 2010 8:25 am; Thanked: 3 times

by Ramit88 » Fri Jan 07, 2011 11:32 pm

is one a multiple of every number?

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anshumishra: Legendary Member; Posts: 543; Joined: Tue Jun 15, 2010 7:01 pmFollowed by: 3 members; Thanked: 147 times

by anshumishra » Fri Jan 07, 2011 11:35 pm

Ramit88 wrote:is one a multiple of every number?

Nope, but every no. is multiple of one. If you get (say) no. 2 on the 1st dice and no. 1 on 2nd dice, still you win. (As the number showing on one of the dice is still a multiple of number showing on the other).

Thanks
Anshu

(Every mistake is a lesson learned )

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