Question

Imagine rolling a fair​ six-sided die three times.
a. What is the theoretical probability that all three rolls of the die show a 5 on​ top?
b. What is the theoretical probability the first roll of the die shows a 4 and the next two rolls show a 5 on​ top?

Answer 1

first
answer this
what is the probability of throwing 5 on the first throw

second
answer this
are the results of the three throws independent?

then we can proceed...

Answer 2

a)
You roll 3 times so that's like 3 places:

_ _ _

It asks for the probability with 5 on top, and that's 1 time for each.

(1/6) (1/6) (1/6)

Multiply them together to get the probability. I prefer a tree diagram but too lazy to draw it :b

b) Probability of 4 on the first roll is (1/6)
Probability of next two rolls being a 5 is (1/6)(1/6)

So (1/6) * (1/6) * (1/6) as well. Same thing.

This isn't conditional probability, so the latter rolls aren't changed.