If two loaded dice each have the property that $$2$$ or $$4$$ is three times as likely to appear as $$1$$, $$3$$, $$5$$ or $$6$$ on each roll. When two such dice are rolled, the probability of obtaining a total of $$7$$ is p then the value of $$1/pis$$ (where$$ [.] represents the greatest integer $$function)

Question

If two loaded dice each have the property that $$2$$ or $$4$$ is three times as likely to appear as $$1$$, $$3$$, $$5$$ or $$6$$ on each roll. When two such dice are rolled, the probability of obtaining a total of $$7$$ is p then the value of $$1/pis$$ (where$$ [.] represents the greatest integer $$function)

Infinity Learn · Accepted Answer

Let the probability 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 $$4p+6p=1$$⇒$$p=110$$∴ $$P(1)=P(3)=P(5)=P(6)=110$$; and $$P(2)=P(4)=310Required$$ probability $$p=P($$ total of $$7$$ with a draw of $$dice)$$ $$p=P($$ total of $$7$$ with a draw of dice $$)=P(16$$,$$61$$,$$25$$,$$52$$,$$43$$,$$34)=2110$$⋅$$110+2310$$⋅$$110+2310$$⋅$$110=2+6+6100=14100=750$$

Theorems of probability

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If two loaded dice each have the property that 2 or 4 is three times as likely to appear as 1, 3, 5 or 6 on each roll. When two such dice are rolled, the probability of obtaining a total of 7 is p then the value of $[1 / p]$ is (where [.] represents the greatest integer function)

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Theorems of probability

Remember concepts with our Masterclasses.

If two loaded dice each have the property that 2 or 4 is three times as likely to appear as 1, 3, 5 or 6 on each roll. When two such dice are rolled, the probability of obtaining a total of 7 is p then the value of 1/pis (where [.] represents the greatest integer function)

Ready to Test Your Skills?

free study material

If two loaded dice each have the property that 2 or 4 is three times as likely to appear as 1, 3, 5 or 6 on each roll. When two such dice are rolled, the probability of obtaining a total of 7 is p then the value of $[1 / p]$ is (where [.] represents the greatest integer function)