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Probability - Challenge

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gmatrant: Master | Next Rank: 500 Posts; Posts: 416; Joined: Wed Oct 03, 2007 9:08 amFollowed by: 1 member; Thanked: 10 times

by gmatrant » Sat Oct 13, 2007 9:44 pm

On a biased die, an even number appears three times as frequently as an odd number. If the die is thrown twice, what is the probability that the sum is 10 or more?

1) 15/37 2) 17/72 3)35/72 4)23/37

Answer: [spoiler](2)[/spoiler]

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Source: Beat The GMAT — Problem Solving | Sat Oct 13, 2007 9:44 pm

samirpandeyit62: Master | Next Rank: 500 Posts; Posts: 460; Joined: Sun Mar 25, 2007 7:42 am; Thanked: 27 times

by samirpandeyit62 » Mon Oct 15, 2007 7:27 am

Now a die has 3 odd nos 1,3,5 & 3 even 2,4,6

now even is three times more likely that odd

now we need to normalise the probabilties

we can say 3*3 + 1+1+1 =12 is the normalising factor (3:1 proportion)

i.e so P of 1,3,5 =1/12 & P of 2,4,6 = 3/12

so here the scenario's are

5,5 4,6 6,4 5,6 6,5 6,6

so reqd probabilty is

1/12 *1/12 + 3(3/12*3/12) + 2(1/12*3/12)

1/144 +27/144 + 6/144

=34/144

= 17/72

Ans B (2)

Regards
Samir

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