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With a fair die, the probability of rolling any number 1 through 6 is the same. If P(1) represents the probability of rolling a 1, P(2) the probability of rolling a 2, and so forth, what is the value of: P(1) P(2) P(3) P(4) P(5) P(6)?.

Answer :

ashishdwivedilVT

Using probability theory, the value of P(1) P(2) P(3) P(4) P(5) P(6) is [tex](1/6)^{6}[/tex].

What is probability?

Probability is the measurement of possibilities or chances.

Probability = [tex]\frac{FavourableOutcomes}{TotalOutcomes}[/tex]

In case of a die, favorable outcomes are 1 or 2 or 3 or 4 or 5 or 6 i.e. 1

Total outcomes are {1,2,3,4,5,6} ie 6

From the above formula,

Probability P(1) of rolling a 1 = 1/6

Probability P(2) of rolling a 2 = 1/6

Probability P(3) of rolling a 3 = 1/6

Probability P(4) of rolling a 4 = 1/6

Probability P(5) of rolling a 5 = 1/6

Probability P(6) of rolling a 6 = 1/6

P(1)P(2)P(3)P(4)P(5)P(6) = [tex]\frac{1}{6} *\frac{1}{6}*\frac{1}{6}*\frac{1}{6}*\frac{1}{6}*\frac{1}{6} = (\frac{1}{6} )^{6}[/tex]

Therefore, the value of P(1) P(2) P(3) P(4) P(5) P(6) is [tex](1/6)^{6}[/tex].

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