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?

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)\\)?

if two fair dice are rolled, there are two different ways to roll a sum of 3:
\

$$\begin{array}{|c|c|} \\hline \\text{die 1} & \\text{die 2} \\\\ \\hline 1 & 2 \\\\ \\hline 2 & 1 \\\\ \\hline \\end{array}$$

how many different ways are there to roll a sum of 4?

when rolling two fair dice, the probability of rolling different sums is

• the same
• different

Explanation:

Calculate single die probability

Using the Theoretical Probability and Sample Space knowledge points

$$
LATEXBLOCK0
$$

Sum of probabilities of all outcomes

Using the Probability Axioms and Sample Space Probability knowledge points

$$
LATEXBLOCK1
$$

Find ways to roll a sum of 4

Using the Sample Space and Favorable Outcomes knowledge points

$$
LATEXBLOCK2
$$

Analyze probability of different sums

Using the Theoretical Probability and Sample Space knowledge points

$$
LATEXBLOCK3
$$

Answer:

Question 1

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?
<blank>\(1/6\)</blank>

Question 2

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 \(P(1) + P(2) + P(3) + P(4) + P(5) + P(6)\)?
<blank>1</blank>

Question 3

How many different ways are there to roll a sum of 4?
<blank>3</blank>

Question 4

When rolling two fair dice, the probability of rolling different sums is

• the same
• different (Correct answer)