Question

What is the probability that a triple will occur within the first five rolls of three dice?

Answer 1

There are 6^3 possible outcomes when rolling 3 fair dice. There are 6 possible outcomes that are a triple; 111, 222, 333, 444, 555 and 666. Therefore the probability of a triple in one roll of the dice is 6/6^3 = 1/36.
The probability of exactly one triple within the first five rolls of the three dice is found using the binomial distribution as follows:
\[P(1\ triple\ out\ of\ 5\ rolls)=5C1 \times (\frac{1}{36})^{1} \times (\frac{35}{36})^{4}\]
\[=4\times0.027778\times0.893433=you\ can\ calculate\]

Answer 2

Correction: The calculation is as follows:\[5\times0.027778\times0.893433\]

Answer 3

Just think of it this way:

Prob(triple will occur during first 5 rolls) = 1 - Prob(triple WILL NOT OCCUR)

Since the probability that a triple won't occur in a given roll is:
\[= (\frac{ 35 }{ 36 })\]
And, since each roll is an independent event, the probability of no triples in the first five rolls is:
\[= (\frac{ 35 }{ 36 })^{5} = 86.86%\]

Therefore, the probability that there WILL be AT LEAST one triple rolled is equal to:

1 - 0.8686 = .1314
= 13.14 %

Note: This is a little bit higher than Kropot's answer since your question says nothing about one and ONLY ONE triple but rather AT LEAST one triple occurs.

Also, for this type of problem you want to use the GEOMETRIC distribution....

Answer 4

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