Question

You wish to roll a 7 on and 8-sided die. What is the probability that the first 7 happens on the 3rd, 4th, or 5th try?

Answer 1

0.15%

Explanation:

The probability of rolling a 7 on a 8-sided die will always be:

`1/8`

We know that for the first two tries that there is 7/8 chance that the die will land on anything but a 7:

`=(7/8)\cdot{(7/8)}=49/64=0.77`

For the die to land on a 7 the 3rd, 4th and 5th try is:

`=(1/8)\cdot{(1/8)}\cdot{(1/8)}=1/512`

The probability is therefore:

`{1/512)\cdot{(49/64)}=49/32768=0.00149`

The probability that the die will land on a 7 not on the first and second try but on the 3rd, 4th and 5th try is 0.15%