Question

Statistics

Posted about 2 months ago

```
Anna, Irina, Avel, and Vlad are going on a road trip. The following table shows an incomplete probability model for who will be driving during any given kilometer.
\begin{tabular}{cc}
Person & Probability \\
\hline Anna & $\frac{1}{8}$ \\
Irina & $\frac{3}{8}$ \\
Avel & $?$ \\
Vlad & $\frac{1}{8}$
\end{tabular}
What is the probability that Avel will be driving during any given kilometer?
Choose 1 answer:
(A) $\frac{1}{8}$
(B) $\frac{3}{8}$
(c) $\frac{5}{8}$
() $\frac{8}{8}$
```

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Answer from Sia

Verified answer

Posted about 2 months ago

Solution by Steps

step 1

To find the probability that Avel will be driving, we need to ensure that the sum of all probabilities in the table equals 1

step 2

The given probabilities are:
$P(\text{Anna}) = \frac{1}{8}, \quad P(\text{Irina}) = \frac{3}{8}, \quad P(\text{Vlad}) = \frac{1}{8}$

step 3

Let $P(\text{Avel}) = x$. The sum of all probabilities should be:
$\frac{1}{8} + \frac{3}{8} + x + \frac{1}{8} = 1$

step 4

Simplify the equation:
$\frac{1}{8} + \frac{3}{8} + \frac{1}{8} + x = 1$
$\frac{5}{8} + x = 1$
$x = 1 - \frac{5}{8}$
$x = \frac{3}{8}$

Answer

B

Key Concept

Sum of probabilities in a probability model

Explanation

The sum of all probabilities in a probability model must equal 1. By solving the equation, we find that the probability for Avel is $\frac{3}{8}$.

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