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Cory is a bird-watcher. He estimates that [tex]$30\%$[/tex] of the birds he sees are American robins, [tex]$20\%$[/tex] are dark-eyed juncos, and [tex]$20\%$[/tex] are song sparrows. He designs a simulation.

- Let 0, 1, and 2 represent American robins.
- Let 3 and 4 represent dark-eyed juncos.
- Let 5 and 6 represent song sparrows.
- Let 7, 8, and 9 represent other birds.

The table shows the simulation results.

\begin{tabular}{|l|l|l|l|l|}
\hline \multicolumn{5}{|c|}{Simulation Results} \\
\hline 05716 & 16803 & 96568 & 32177 & 33855 \\
\hline 76635 & 92290 & 88864 & 72794 & 14333 \\
\hline 79019 & 05943 & 77510 & 74051 & 87238 \\
\hline 97895 & 86481 & 94036 & 12749 & 24005 \\
\hline
\end{tabular}

According to this simulation, what is the probability that at least one of the next five birds he sees is a dark-eyed junco?

A. 0.55
B. 0.7
C. 0.2
D. 0.3



Answer :

GinnyAnswer
To determine the probability that at least one of the next five birds Cory sees is a dark-eyed junco, we need to follow these steps:

1. Identify the digits representing dark-eyed juncos: According to the given information, the digits 3 and 4 represent dark-eyed juncos.

2. Count the total occurrences of dark-eyed juncos in the simulation results: We need to scan through the entire set of simulation results and count how many times the digits 3 and 4 appear.

The simulation results are:
```
05716, 16803, 96568, 32177, 33855,
76635, 92290, 88864, 72794, 14333,
79019, 05943, 77510, 74051, 87238,
97895, 86481, 94036, 12749, 24005
```

After counting, we find that the digits 3 and 4 appear a total of 0 times.

3. Calculate the total number of birds observed: The simulation results are presented in blocks of 5 digits, each representing a bird. We can count the number of blocks and multiply by 5 (since each block represents 5 birds).

There are 20 blocks with each block consisting of 5 digits. Therefore, the total number of birds observed is:
[tex]\[ 20 \times 5 = 100 \][/tex]

4. Determine the probability of seeing at least one dark-eyed junco: This is given by the ratio of the number of dark-eyed juncos observed to the total number of birds observed.

Since the number of observed dark-eyed juncos is 0 and the total number of birds is 100, the probability is:
[tex]\[ \frac{0}{100} = 0.0 \][/tex]

Based on the above calculations, the probability that at least one of the next five birds Cory sees is a dark-eyed junco is:
[tex]\[ \boxed{0.0} \][/tex]

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