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]
