A person visiting Las Vegas rolls the dice at a "craps" table and wonders what is the probability of rolling the dice 24 times without ever rolling a "7". Can the binomial distribution be applied to this situation?

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Answer 1 · 2016-07-14T13:10:08

Yes

Two dice has a probability of rolling a 7 only #2/36# ways
So rolling a dice with no 7 is the same as

#34/36 #. The probability of the 7 not landing twice in a row is #34/36*34/36# and 24 times is #(34/36)^24#

If we used the binomial distribution we would say

#nCk * rho^k(1- rho)^(n-k)# thus the result would be

#((24!)/((24-24)!24!)) (34/36)^24(1-34/36)^(24-24)#

#((24!)/(24!)) (34/36)^24(1-34/36)^(0)#

you will notice that the only thing that remains is
#(34/36)^24#

so yes you can use it.