# Probability confusion

Homework Statement
How many times do we need to roll a fair die to get a better than evens chance of at least one six?

The attempt at a solution
Let n be the number of rolls. Am I trying to find how large n must be so P(At least one six)≥ 1/2?
I'm working on the basis that I need to solve the probability of the union of events Ai, where Ai denotes the event of rolling i sixes, i =1,2,3...., being greater than 1/2.
Any help or nudge in the right direction will be appreciated.

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phinds
Gold Member
2019 Award
I'd attack it by finding the odds of NOT getting a six with one roll, then 2 rolls, then 3 rolls, and so on. As soon as that probability drops below 50% you've got the answer.

pasmith
Homework Helper
Homework Statement
How many times do we need to roll a fair die to get a better than evens chance of at least one six?

The attempt at a solution
Let n be the number of rolls. Am I trying to find how large n must be so P(At least one six)≥ 1/2?
I'm working on the basis that I need to solve the probability of the union of events Ai, where Ai denotes the event of rolling i sixes, i =1,2,3...., being greater than 1/2.
Any help or nudge in the right direction will be appreciated.
P(at least one six) = 1 - P(no sixes)

phinds