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)?
done

Explanation:

Step1: Recall probability rules

For a fair die, each outcome (1 - 6) is mutually exclusive and collectively exhaustive. The sum of probabilities of all possible outcomes in a sample space is 1.

Step2: Apply the rule

Since \(P(1), P(2), \dots, P(6)\) are the probabilities of all possible outcomes when rolling a die, their sum \(P(1)+P(2)+P(3)+P(4)+P(5)+P(6)\) must equal 1. Also, since each \(P(i)=\frac{1}{6}\) for \(i = 1,2,\dots,6\), we can calculate: \(\frac{1}{6}+\frac{1}{6}+\frac{1}{6}+\frac{1}{6}+\frac{1}{6}+\frac{1}{6}=\frac{6}{6}=1\).

Answer:

1