Question

Two six-sided dice are rolled and the sum of the faces showing is recorded after each roll. Let $X=$the number of rolls required until a sum greater than $7$is obtained. If $100$trials are conducted, which of the following is most likely to be part of the probability distribution of $X$?

Short answer

Option (a) is most likely to be part of the probability distribution of$X$.

Step-by-step solution

Given information

We have been given that two six-sided dice are rolled. We are asked to record the sum of the faces after each roll. It is also given that let $X=$the number of rolls required until a sum greater than $7$is obtained.

We need to find the option which is most likely to be the probability distribution of $X$if $100$trials are conducted.

Explanation

The option (b) is incorrect because we cannot get a sum greater than $7$by having $0$rolls.

We have observed that it needs only $1$roll to get a sum greater than $7$in majority of the cases because the probability of doing this is very high and the probability of not doing this is more improbable on the first try.