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three fair dice are rolled together. what is the probability [#permalink]
 26 Jun 2003, 00:25
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three fair dice are rolled together. what is the probability of NOT having exactly 2 fives.
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Manager
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The probability of having exactly 2 fives is 3/216
Therefore, the probability of NOT getting exactly 2 fives is 1-(3/216)=98.6%
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Manager
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My apologies - my last answer was not correct.
The correct answer is (1-5/72)
The probability of having exactly two fives is 3C2*1/6*1/6*5/6=5/72
Therefore, the probability of NOT having exactly two fives is 1-5/72 = 93.1%
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Ohhh... guys.... so many mistakes!!!
P (exactly 2 fives out of 3 dice) = 1/6*1/6*5/6*3C1=15/216
P (NOT having) = 1–(15/216)=201/216=67/72
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Intern
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I understood 1/6*1/6*5/6, and thus came up with 5/216. Of coz, then 1- 5/216.
But why multiply it into 3C1?!!!!! Pls explain. Thanks 
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GMAT Instructor
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sunitha wrote: I understood 1/6*1/6*5/6, and thus came up with 5/216. Of coz, then 1- 5/216. But why multiply it into 3C1?!!!!! Pls explain. Thanks You correctly calculated the number of ways that a 5 could come up in the first and second slots, or 5 5 X. However, there are two other ways you can get 2 fives. X 5 5 and 5 X 5. Hence, you need to multiple the number of ways to get a SPECIFIC pairing of 2 5's (which you did), by all the different ways to get 2 5's from 3 dice, which is 3C2 = 3.
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AkamaiBrah
Former Senior Instructor, Manhattan GMAT and VeritasPrep
Vice President, Midtown NYC Investment Bank, Structured Finance IT
MFE, Haas School of Business, UC Berkeley, Class of 2005
MBA, Anderson School of Management, UCLA, Class of 1993
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Manager
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AkamaiBrah wrote: sunitha wrote: I understood 1/6*1/6*5/6, and thus came up with 5/216. Of coz, then 1- 5/216. But why multiply it into 3C1?!!!!! Pls explain. Thanks You correctly calculated the number of ways that a 5 could come up in the first and second slots, or 5 5 X. However, there are two other ways you can get 2 fives. X 5 5 and 5 X 5. Hence, you need to multiple the number of ways to get a SPECIFIC pairing of 2 5's (which you did), by all the different ways to get 2 5's from 3 dice, which is 3C2 = 3. so it should be multiplied with 3c2, not 3c1 as stolyar says.
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stolyar wrote: KSS wrote: AkamaiBrah wrote: sunitha wrote: I understood 1/6*1/6*5/6, and thus came up with 5/216. Of coz, then 1- 5/216. But why multiply it into 3C1?!!!!! Pls explain. Thanks You correctly calculated the number of ways that a 5 could come up in the first and second slots, or 5 5 X. However, there are two other ways you can get 2 fives. X 5 5 and 5 X 5. Hence, you need to multiple the number of ways to get a SPECIFIC pairing of 2 5's (which you did), by all the different ways to get 2 5's from 3 dice, which is 3C2 = 3. so it should be multiplied with 3c2, not 3c1 as stolyar says. 3C2=3C1=3 you should have known about it. You bet. I should have.
Dumb me. 
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