Probability roll 44 before 45

Question

espp · Accepted Answer

Consecutive: P(44 before 45) = P(4 before 5) = 0.5.
Not consecutive: P(44 before 45) = p_s = 5/6*p_s + 1/6*p_4 --> p_s = p_4, p_4 = 1/6*1 + 1/6*0 + 4/6*p_4 --> 2/6*p_4 = 1/6 --> p_4 = 1/2 so P(44 before 45) = 0.5. In either case, you have a 50% chance of seeing 44 before 45 (assuming a d6).

Gas · Answer

For consecutive it's not 50/50

Dan · Answer

I agree if its consecutive it should be 50/50
If not consecutive is it correct to only consider the numbers 4 and 5 as these are the only numbers of interest, then it is as if we are flipping a coin where 4 is heads and 5 is tails, then the question becomes whats the prob of getting two heads before both a heads and tails , in two flips we can get HH, TH, HT or TT
so p=1/4 + 1/4p
3/4p=1/4
p=1/3
Does this seem right

anon · Answer

Assuming this means a rolling a consecutive 4-4 vs a 4-5 on a six sided die, wouldn't this simply be a 50/50? After rolling the first 4, there is an equal probability of getting another 4 or 5, with either of these cases ending the trial immediately.

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