Geometry John is playing around with probabilities and thinking about rolling a die until he gets a 6. He computes that (5/6) 4 is equal to 0.4823, and concludes, “Cool, I’ve got a better than 50%...

Geometry John is playing around with probabilities and thinking about rolling a die until he gets a 6. He computes that (5/6)⁴
is equal to 0.4823, and concludes, “Cool, I’ve got a better than 50% chance of seeing my first six by my fourth roll.” Then Geometry John wonders, “if I roll a die until I roll two sixes, do I have a better than 50% chance of seeing my second six by my
eighth roll?” What is the answer to Geometry John’s question? Compute the probability.