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)? )

Question

Accepted Answer

# Explanation:
## Step1: Recall the probability formula
The probability formula is $P(A)=\frac{\text{Number of favorable outcomes}}{\text{Total number of outcomes}}$. For a fair die, the total number of outcomes when rolled is $n = 6$ (the numbers $1,2,3,4,5,6$).
## Step2: Calculate each $P(i)$
For $P(1)$, the number of favorable outcomes (rolling a $1$) is $m_1=1$. So $P(1)=\frac{1}{6}$. Similarly, $P(2)=\frac{1}{6}$, $P(3)=\frac{1}{6}$, $P(4)=\frac{1}{6}$, $P(5)=\frac{1}{6}$, and $P(6)=\frac{1}{6}$.
## Step3: Sum up the probabilities
$$
\begin{align*}
P(1)+P(2)+P(3)+P(4)+P(5)+P(6)&=\frac{1}{6}+\frac{1}{6}+\frac{1}{6}+\frac{1}{6}+\frac{1}{6}+\frac{1}{6}\
&=\frac{1 + 1+1+1+1+1}{6}\
&=\frac{6}{6}
\end{align*}
$$

# Answer:
$1$

Sovi.AI - AI Math Tutor

QUESTION IMAGE

Question

Explanation:

Step1: Recall the probability formula

Step2: Calculate each \(P(i)\)

Step3: Sum up the probabilities

Answer: