To determine which score is most likely, we need to analyze the given probability distribution. The table provides the probabilities associated with each score as follows:
[tex]\[
\begin{array}{|c|c|}
\hline
\multicolumn{2}{|c|}{\text{Probability Distribution}} \\
\hline
\text{Score: } X & \text{Probability: } P(X) \\
\hline
1 & 0.06 \\
\hline
2 & 0.20 \\
\hline
3 & 0.48 \\
\hline
4 & 0.26 \\
\hline
\end{array}
\][/tex]
To find out the most likely score, we examine the probabilities for each score:
- The probability of scoring 1 is [tex]\(0.06\)[/tex],
- The probability of scoring 2 is [tex]\(0.20\)[/tex],
- The probability of scoring 3 is [tex]\(0.48\)[/tex],
- The probability of scoring 4 is [tex]\(0.26\)[/tex].
Among these probabilities, [tex]\(0.48\)[/tex] is the highest probability.
Therefore, the score [tex]\(3\)[/tex] is the most likely score because it has the highest probability of occurring, which is [tex]\(0.48\)[/tex].
