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As a coach for the local soccer team, you want your team to score a goal in the next big game. You look back on last year's stats to make a prediction. The data is shown below.

\begin{tabular}{|l|l|}
\hline Matches & Goals Scored \\
\hline Match 1 & 1 \\
\hline Match 2 & 1 \\
\hline Match 3 & 2 \\
\hline Match 4 & 2 \\
\hline Match 5 & 3 \\
\hline Match 6 & 0 \\
\hline Match 7 & 4 \\
\hline Match 8 & 4 \\
\hline Match 9 & 4 \\
\hline Match 10 & 2 \\
\hline Match 11 & 2 \\
\hline Match 12 & 1 \\
\hline
\end{tabular}

Determine the probability of your team scoring no goals.
[tex]$
P(X=0)=
$[/tex]
[tex]$\qquad$[/tex]



Answer :

GinnyAnswer
To determine the probability of my team scoring no goals, let's follow a structured approach using the data provided:

1. Count the total number of matches played:
- The data specifies that there are statistics for 12 matches in total.

2. Count how many matches resulted in scoring no goals:
- Reviewing the data, the matches and their corresponding goals scored are:
- Match 1: 1 goal
- Match 2: 1 goal
- Match 3: 2 goals
- Match 4: 2 goals
- Match 5: 3 goals
- Match 6: 0 goals
- Match 7: 4 goals
- Match 8: 4 goals
- Match 9: 4 goals
- Match 10: 2 goals
- Match 11: 2 goals
- Match 12: 1 goal
- From this, only Match 6 ended with 0 goals scored.

3. Calculate the number of matches with no goals scored:
- There is only 1 match where no goals were scored.

4. Calculate the probability:
- Probability [tex]\(P(X=0)\)[/tex] is the number of matches with no goals divided by the total number of matches:
[tex]\[ P(X=0) = \frac{\text{Number of matches with 0 goals}}{\text{Total number of matches}} \][/tex]
Substituting the numbers from the data:
[tex]\[ P(X=0) = \frac{1}{12} \][/tex]

5. Simplify the fraction to a decimal:
- [tex]\(\frac{1}{12}\)[/tex] as a decimal is approximately 0.0833...

Therefore, the probability [tex]\(P(X=0)\)[/tex] of my team scoring no goals in the next game is:
[tex]\[ P(X=0) = 0.0833\overline{3} \][/tex]

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