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A local charity holds a carnival to raise money. In one activity, participants make a [tex]$3 donation for a chance to spin a wheel that has 10 spaces with the values 0, 1, 2, 5, and 10. Whatever space it lands on, the participant wins that value. Let $[/tex]X$ represent the value of a random spin. The distribution is given in the table.

\begin{tabular}{|c|c|c|c|c|c|}
\hline
\begin{tabular}{c}
Value of a \\
Spin
\end{tabular} & 0 & 1 & 2 & 5 & 10 \\
\hline
Probability & 0.4 & 0.2 & 0.2 & 0.1 & 0.1 \\
\hline
\end{tabular}

What is the probability that the value is at most 2?

A. 0.2
B. 0.4
C. 0.6
D. 0.8



Answer :

GinnyAnswer
To find the probability that the value of a spin on the wheel is at most 2, we need to sum up the probabilities of all outcomes where the value is 0, 1, or 2.

The table provided gives us the following probabilities:

- Probability of landing on 0: [tex]\(0.4\)[/tex]
- Probability of landing on 1: [tex]\(0.2\)[/tex]
- Probability of landing on 2: [tex]\(0.2\)[/tex]

To determine the total probability that the value is at most 2, we sum these individual probabilities:

[tex]\[ \text{Probability at most 2} = \text{Probability of 0} + \text{Probability of 1} + \text{Probability of 2} \][/tex]

Substituting the given values:

[tex]\[ \text{Probability at most 2} = 0.4 + 0.2 + 0.2 \][/tex]

[tex]\[ \text{Probability at most 2} = 0.8 \][/tex]

Thus, the probability that the value of a spin is at most 2 is [tex]\(0.8\)[/tex].

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