My name is Tony and I'm a senior at Memorial High. My question is; When rolling 2 dice, what is the probability of rolling 5 sevens before rolling a six or an eight?
The probability of rolling a seven is 6/36
Suppose that the fifth 7 is rolled on the nth roll and none of the previous n - 1 rolls is a five or an eight. This string of n - 1 rolls then consists of 4 sevens and n - 5 outcomes that are not fives or eights. The probability of this arrangement in n - 1 rolls is
n can be any positive integer larger than 4 and hence the probability of rolling 5 sevens before rolling a six or an eight is
You can evaluate this expression if you know Newton's form of the binomial theorem. If |x| < 1