maths challenge (continued)?

Question

We can reframe the question : A die is rolled untill 6 point is found.
What are the chances of getting 1 point in x number of attempts?
if x=1 the answer is 1/6
what are the values for x=2 ,3, 4 ....?

In the original question the if 1 is found the result is known as 6 will be definitely found at infinity.

Answer 1

Greetings

So if we roll and don't get 6 point then the chance is 5/6

x = 2 , p =5/6*1/6
x = 3 , p =5/6*5/6*1/6
x = n , p =(5/6)^(n-1)*1/6

The total probablity is the sum of the series

p = 1/6 + 5/6*1/6 + ... 1/6*(5/6)^(n-1) up to n rolls of the die

p =1 when we take the sum of the infinite series

p = 1/6 /(1 -5/6) = 1/6 / 1/6 = 1

Regards