What are the odds and probability of rolling 5 dice, and all 5 dice are the same number?

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What are the odds and probability of rolling 5 dice, and all 5 dice are the same number?

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Answer 1 · 2016-06-27T07:32:55

$1/6^4=1/1296$

Explanation:

There are six faxes with six distinct numbers. For each dice, the
probability is (number of favorable cases)/(the total number of all possible cases).
Because any first roll is favorable, this probability can be modeled by:
$=6*1/(6^(n)$ or $1/(6^(n-1))$

For all showing the same number, it is the compound probability
= product of the separate probabilities.
$=1/(6^(5-1))$
$=1/6^4$

Answer 2 · 2018-05-07T06:52:04

$P("all 5 dice show the same number") = 1/1296$

Odds are $1:625$

Explanation:

Let's look at the probability first.

$P(5 " dice give the same number")$

They must be all $1s$ or all $2s$ or all $3s$ ... and so on

$=P(1,1,1,1,1) +P(2,2,2,2,2)+......... + P(6,6,6,6,6)$

$(1/6xx1/6xx1/6xx1/6xx1/6) + ....+(1/6xx1/6xx1/6xx1/6xx1/6)$

$= 1/6^5 + 1/6^5 + .......... +1/6^5$

$= 6 xx 1/6^5$

$=1/6^4 = 1/1296$

The odds are given as a ratio of the number of ways this will happen compared to the number of ways it doesn't.

So if the first die is $1$ , the other four will not be,

$6 xx (1/6 xx5/6xx5/6xx5/6xx5/6) = 625/1296$

The odds for this happening are $1 : 625$

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What are the odds and probability of rolling 5 dice, and all 5 dice are the same number?

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