Rolling a Fair Die: Probability of Getting At Least One Six After Multiple Rolls

[Amannequin]

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.

 

[phinds]

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 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]

P(at least one six) = 1 - P(no sixes)

Ah ... isn't that what I just said?