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Determine the probability distribution's missing value. The probability that a tutor will see [tex]\(0, 1, 2, 3\)[/tex] students.

\begin{tabular}{|c|c|c|c|c|c|}
\hline
[tex]$x$[/tex] & [tex]$0$[/tex] & [tex]$1$[/tex] & [tex]$2$[/tex] & [tex]$3$[/tex] & [tex]$4$[/tex] \\
\hline
[tex]$P(x)$[/tex] & [tex]$?$[/tex] & [tex]$0.15$[/tex] & [tex]$0.20$[/tex] & [tex]$0.20$[/tex] & [tex]$0.25$[/tex] \\
\hline
\end{tabular}

ROUND TO TWO DECIMAL PLACES

[tex]\[P(0) = \square\][/tex]



Answer :

GinnyAnswer
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].

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