Probability of getting # 1

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Vemuri: Legendary Member; Posts: 682; Joined: Fri Jan 16, 2009 2:40 amFollowed by: 1 member; Thanked: 32 times

by Vemuri » Sun Mar 22, 2009 8:05 am

When a die that has one of six consecutive integers on each of its sides is rolled twice, what is the probability of getting the number 1 on both rolls?

1. The probability of NOT getting an eight is 1.
2. The probability of NOT getting a seven is 25/36.

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Source: Beat The GMAT — Data Sufficiency | Sun Mar 22, 2009 8:05 am

DanaJ: Site Admin; Posts: 2567; Joined: Thu Jan 01, 2009 10:05 amFollowed by: 550 members; Thanked: 712 times; GMAT Score:770

by DanaJ » Sun Mar 22, 2009 8:23 am

1. tells us that 8 is not on the sides of the dice, since we're 100% sure that 8 can't be there. However, this doesn't help establish whether 1 is on the sides of the dice. Consider these possibilities for the sides of the dice:
a. 1, 2, 3, 4, 5, 6
b. 9, 10, 11, 12, 13, 14

In both cases, 8 isn't there. This is why 1 is insufficient.

2. tells us that 7 is indeed on one of the sides of the dice. This, IMHO, is sufficient to answer your question, since anyway you take it, 1 is "too far away" from 7. Consider the best case: 7 and the numbers immediately smaller than 7:
You get 7, 6, 5, 4, 3, 2 and then you need to stop, since you already have 6 numbers: you are just one number short from 1.

This is why the answer is IMO B

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