To determine the missing probability [tex]\( P(0) \)[/tex], we need to use the fact that the sum of all probabilities in a probability distribution must equal 1. This ensures that one of the outcomes must occur.
Given the probabilities for [tex]\( P(1) \)[/tex], [tex]\( P(2) \)[/tex], [tex]\( P(3) \)[/tex], and [tex]\( P(4) \)[/tex]:
[tex]\[
P(1) = 0.15 \\
P(2) = 0.20 \\
P(3) = 0.20 \\
P(4) = 0.25
\][/tex]
First, we sum these given probabilities:
[tex]\[
P(1) + P(2) + P(3) + P(4) = 0.15 + 0.20 + 0.20 + 0.25
\][/tex]
Calculating the sum:
[tex]\[
0.15 + 0.20 = 0.35 \\
0.35 + 0.20 = 0.55 \\
0.55 + 0.25 = 0.80
\][/tex]
We know that the total of all probabilities should be 1. Therefore, [tex]\( P(0) \)[/tex] can be found by subtracting the sum of the given probabilities from 1:
[tex]\[
P(0) = 1 - (P(1) + P(2) + P(3) + P(4)) = 1 - 0.80 = 0.20
\][/tex]
Therefore, the missing probability rounded to two decimal places is:
[tex]\[
P(0) = 0.20
\][/tex]
So, [tex]\( P(0) = 0.20 \)[/tex].
