To find the probability [tex]\( P(3) \)[/tex] using the data from the provided table, follow these steps:
1. Identify the value of [tex]\( X \)[/tex] for which you need to find the probability. In this case, you need to find [tex]\( P(3) \)[/tex], which means [tex]\( X = 3 \)[/tex].
2. Look for the corresponding probability value [tex]\( P(X) \)[/tex] in the table where [tex]\( X = 3 \)[/tex].
Here is the table again for reference:
[tex]\[
\begin{array}{|c|c|}
\hline
X & P(X) \\
\hline
0 & 0.1 \\
\hline
1 & 0.2 \\
\hline
2 & 0.4 \\
\hline
3 & 0.2 \\
\hline
4 & 0.1 \\
\hline
\end{array}
\][/tex]
3. From the table, locate the row where [tex]\( X = 3 \)[/tex]. The corresponding probability [tex]\( P(X) \)[/tex] is [tex]\( 0.2 \)[/tex].
Therefore, the probability [tex]\( P(3) \)[/tex] is [tex]\( 0.2 \)[/tex].
