Question

You throw a die repeatedly until you get a 6. What is the probability that you need
to throw more than 20 times to get 6?

Answer 1

Throwing a die more than 20 times to get 6 means that 20 times you do not get 6. The probability of not getting 6 once is $\frac{5}{6}$. The probability of not getting 6 during 20 times is $(\frac{5}{6})^{20} = \frac{95367431640625}{3656158440062976}$ which is the answer.