A fair die is rolled until the first time 6 appears. What is the probability that an even number of rolls is needed? With this knowledge, how many times would you expect to roll the die before all six sides appeared at least once?
Asked
Active
Viewed 14 times
0
-
Have you tried anything on this? Can you set up an infinite sum perhaps that describes the scenario? Are you having difficulty evaluating that infinite sum maybe? Recall... you find a $6$ for the first time after an even number of rolls by either rolling one non-6 followed by a $6$, rolling three non-6's followed by a $6$, or rolling five non-6's followed by a $6$, etc... – JMoravitz Nov 06 '20 at 13:28
-
What is the probability that you first succeed on the first roll? What is the probability that you first succeed on the second roll? How would failing on both rolls change the probability that an even number of rolls is needed? – Henry Nov 06 '20 at 13:31
-
As for the second part of the problem, it sounds like a non-sequitur... unrelated to the earlier part of the problem. I am closing this as a duplicate of that as it is arguably the more difficult of the parts of the question. – JMoravitz Nov 06 '20 at 13:32
-
@JMoravitz I also fail to see how "with this knowledge" might help with what would be a simple coupon-collector problem – Henry Nov 06 '20 at 13:33