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Find the probability of obtaining at least one double-four in six rolls of a pair of...

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user1548464 | eNoter

Posted May 4, 2013 at 6:22 AM via web

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Find the probability of obtaining at least one double-four in six rolls of a pair of tetrahedral dice.

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pramodpandey | College Teacher | Valedictorian

Posted May 4, 2013 at 6:41 AM (Answer #1)

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sample

S={(1,1),(1,2),(1,3),(1,4),(2,1),(2,2),(2,3),(2,4),(3,1),(3,2),(3,3),(3,4),(4,1),(4,2),(4,3),(4,4)}

E=double four

p=P(E)=1/16

q=1-1/16=15/16

P(at least one double four)=1-P(no double four)

P(no doublefour)=`^6C_0(1/16)^0(15/16)^6`

`=(15/16)^6`

P( at least one double four)=`1-(15/16)^6`

`=.321`

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