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 to obtain a sum greater than $7$. If $100$trials are conducted, which of the following is most likely to be the result of the simulation?

a.

b.

c.

d.

e.

Short answer

The correct answer is option (a).

Step-by-step solution

Given information

$X=$the number of rolls required to obtain a sum greater than $7$.

$100$ trials are conducted

Explanation

Two six-sided dice are tossed, with the sum of the faces shown being recorded after each roll.

Then, any choice other than (a) is invalid, because a sum higher than $7$cannot be rolled with $0$rolls.

Because the probability of getting a total larger than$7$ is extremely high, and not doing so on the first try gets increasingly implausible, the majority of trials only require one roll. As a result, option (a) is the proper choice.