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You flip 3 coins 20 times and record the number of heads. The results are listed below.

[tex]\[ 2, 1, 0, 2, 2, 0, 2, 2, 3, 2, 1, 2, 1, 2, 1, 1, 2, 1, 3, 1 \][/tex]

Complete the frequency table.

[tex]\[
\begin{array}{|c|c|}
\hline \text{Number of Heads} & \text{Frequency} \\
\hline 0 & a \\
\hline 1 & b \\
\hline 2 & c \\
\hline 3 & d \\
\hline
\end{array}
\][/tex]

[tex]\[
a = \square
\][/tex]
[tex]\[
b = \square
\][/tex]
[tex]\[
c = \square
\][/tex]
[tex]\[
d = \square
\][/tex]


Sagot :

To determine the frequency of the number of heads when flipping 3 coins 20 times and recording the results, we follow these steps:

1. List the Recorded Results:
The results from flipping the coins 20 times are:
[tex]\[ 2, 1, 0, 2, 2, 0, 2, 2, 3, 2, 1, 2, 1, 2, 1, 1, 2, 1, 3, 1 \][/tex]

2. Count the Frequency for Each Possible Number of Heads:

- Frequency of 0 Heads:
Count how many times '0' appears in the list.
There are 2 occurrences of '0'.
[tex]\[ a = 2 \][/tex]

- Frequency of 1 Head:
Count how many times '1' appears in the list.
There are 7 occurrences of '1'.
[tex]\[ b = 7 \][/tex]

- Frequency of 2 Heads:
Count how many times '2' appears in the list.
There are 9 occurrences of '2'.
[tex]\[ c = 9 \][/tex]

- Frequency of 3 Heads:
Count how many times '3' appears in the list.
There are 2 occurrences of '3'.
[tex]\[ d = 2 \][/tex]

3. Complete the Frequency Table:
Using the counted frequencies, we fill in the table:

\begin{tabular}{|c|c|}
\hline Number of Heads & Frequency \\
\hline 0 & 2 \\
\hline 1 & 7 \\
\hline 2 & 9 \\
\hline 3 & 2 \\
\hline
\end{tabular}

So, the completed table is:

[tex]\[ a = 2,\quad b = 7,\quad c = 9,\quad d = 2 \][/tex]