Statistics Help

Question

A standard six-sided dice is repeatedly rolled until it lands on a two. What is the probability that the first two is rolled after the first six rolls?

Answer 1

You could use the geometric probability distribution or just apply the multiplication rule for independent events.

Let T = Event of rolling a 2, T^c = Event of not rolling a 2.

P(T)=1/6 and P( T^c =5/6.

By independence, the probability the the first two is rolled after first 6 rolls:

P(T^c) * P(T^c) * P(T^c) * P(T^c) * P(T^c) * P(T^c) * P(T) [first 6 rolls, are not 2, then the 7th roll is a 2)

= (5/6)⁶ * (1/6)

= 15625 / 279936

~ 0.0558