The number of cars waiting at a bank for 60 minutes is as follows.

\begin{tabular}{|c|c|c|c|c|c|c|c|c|c|}
\hline
Cars & 0 & 1 & 2 & 3 & 4 & 5 & 6 & 7 & 8 \\
\hline
Frequency & 2 & 9 & 16 & 12 & 8 & 6 & 4 & 2 & 1 \\
\hline
\end{tabular}

Find the probability of 5 cars waiting in line.

[tex]\[ P(5) = \ ? \][/tex]



Answer :

To find the probability of 5 cars waiting in line, we need to follow these steps:

1. Calculate the total frequency of all cars:
The given data shows the number of cars waiting at the bank and their respective frequencies over a 60-minute period.
[tex]\[ \text{Total frequency} = 2 + 9 + 16 + 12 + 8 + 6 + 4 + 2 + 1 \][/tex]

2. Identify the frequency of 5 cars waiting:
From the table, the frequency of 5 cars waiting is 6.

3. Calculate the probability:
The probability of an event is the ratio of the frequency of the event to the total frequency of all events.
[tex]\[ P(5 \text{ cars}) = \frac{\text{Frequency of 5 cars}}{\text{Total frequency}} \][/tex]

4. Substitute the values:
Using the calculated total frequency and the given frequency:
[tex]\[ \text{Total frequency} = 60 \][/tex]
[tex]\[ \text{Frequency of 5 cars} = 6 \][/tex]
[tex]\[ P(5 \text{ cars}) = \frac{6}{60} \][/tex]

5. Simplify the fraction:
[tex]\[ P(5 \text{ cars}) = \frac{6}{60} = 0.1 \][/tex]

Thus, the probability of 5 cars waiting in line is
[tex]\[ P(5) = 0.1 \][/tex]