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

2 Answers

Answer:

#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#

May 7, 2018

Answer:

#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#