Question

Two balanced and fair dice are rolled. One is six-sided and the other is eight-sided.What is the probability of rolling a sum less than 7? Submit the answer as a simplifiedfraction.

Answer 1

Step-by-step explanation

From the statement, we know that:

• we rolled two balanced and fair dice,

,

• one is six-sided and the other is eight-sided.

We want to know the probability of rolling a sum less than 7.

We denote the possible results of rolling the dices as (x, y), where x is the result of the first dice, and y is the result of the second dice. The possible results are:

From this list, we see that the events that sum less than 7 are:

From this list, we see that:

• n(S < 7) = # of results which sum less than 7 = 15,

,

• n(T) = total # of possible results = 6 * 8 = 48.

The probability of rolling a sum less than 7 is:

`P(S<7)=(n(S<7))/(n(T))=(15)/(48)=(5)/(16).`Answer

5/16