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If two loaded dice each have the propert...

If two loaded dice each have the property yjsy 2 or 4 is there times as likely to appears as `1,3,5,or6` on each roll. When two such dice are rolled, the probability of obtaining a total of 7 is p, then value of `[1//p]` is, where `[x]` represents the greatest integer less than or euqal to x.

Text Solution

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The correct Answer is:
7
Let the probaility of the faces `1,3,5` or 6 be p for each face. Hence, probability of each of the faces 2 or 4 is 3p Now according to the question `4p+6p=1`
`impliesp=1/10`
`thereforeP(1)=P(3)=P(5)=P(6)=12/10`
` and P(2)=P(4) =3/10`
`implies` Required probability
p= p (total of 7 with a sraw of dice)
`=P(16,61,25,52,43,34)`
`=2((1)/(10).(1)/(10))+2((3)/(10).(1)/(10))+2((3)/(10).(1)/(10))`
`=(2+6+6)/(100)=14/100=7/50`
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