Question

a fair die is a cube with number 1 through 6 on the sides, represented as painted spots. if a fair die is rolled, what is the probability of number 6 landing face up?
1/6
complete
with a fair die, the probability of rolling any number 1 through 6 is the same.
if p(1) represents the probability of rolling a 1, p(2) the probability of rolling a 2, and so forth, what is the value of: p(1) + p(2) + p(3) + p(4) + p(5) + p(6)? 1
complete
if two fair dice are rolled, there are two different ways to roll a sum of 3:
die 1 | die 2
1 | 2
2 | 1
how many different ways are there to roll a sum of 4?
retry

Explanation:

For the question "How many different ways are there to roll a sum of 4?":

Step1: List possible pairs

We need to find all pairs of numbers \((x,y)\) where \(x\) is the result of Die 1, \(y\) is the result of Die 2, and \(x + y=4\), with \(1\leq x\leq6\) and \(1\leq y\leq6\).

Step2: Find valid pairs

• When \(x = 1\), \(y=4 - 1 = 3\) (so \((1,3)\)).
• When \(x = 2\), \(y=4 - 2 = 2\) (so \((2,2)\)).
• When \(x = 3\), \(y=4 - 3 = 1\) (so \((3,1)\)).

These are all the possible pairs. So there are 3 different ways.

Answer:

3