Question

1. if you roll two six - sided dice, what is the probability of getting a sum of 8?

a. 5/36
b. 2/36
c. 6/36
d. 1/36

Explanation:

Step1: Calculate total number of outcomes

When rolling two six - sided dice, each die has 6 possible outcomes. By the multiplication principle, the total number of outcomes is \(6\times6 = 36\).

Step2: Find number of favorable outcomes

Let the outcomes of the first die be \(x\) and the second die be \(y\). We want \(x + y=8\) where \(1\leq x\leq6\) and \(1\leq y\leq6\).
The pairs \((x,y)\) that satisfy \(x + y = 8\) are \((2,6)\), \((3,5)\), \((4,4)\), \((5,3)\), \((6,2)\). So there are 5 favorable outcomes.

Step3: Calculate probability

The probability \(P\) of an event is given by \(P=\frac{\text{Number of favorable outcomes}}{\text{Total number of outcomes}}\). So \(P=\frac{5}{36}\).

Answer:

A. \(5/36\)