To complete the frequency table, we need to count the occurrences of each possible number of heads (0, 1, 2, and 3) from the list of results. Here are the detailed steps:
1. List of Results:
[tex]\[
[2, 1, 0, 2, 2, 0, 2, 2, 3, 2, 1, 2, 1, 2, 1, 1, 2, 1, 3, 1]
\][/tex]
2. Counting the Number of Heads:
- Number of Heads = 0: Count the zeros in the list.
- Number of Heads = 1: Count the ones in the list.
- Number of Heads = 2: Count the twos in the list.
- Number of Heads = 3: Count the threes in the list.
3. Frequency Calculation:
- Count of zeros (0 heads):
[tex]\[
[2, 1, 0, 2, 2, 0, 2, 2, 3, 2, 1, 2, 1, 2, 1, 1, 2, 1, 3, 1]
\rightarrow \text{There are 2 zeros}
\][/tex]
Thus, [tex]\( a = 2 \)[/tex].
- Count of ones (1 head):
[tex]\[
[2, 1, 0, 2, 2, 0, 2, 2, 3, 2, 1, 2, 1, 2, 1, 1, 2, 1, 3, 1]
\rightarrow \text{There are 7 ones}
\][/tex]
Thus, [tex]\( b = 7 \)[/tex].
- Count of twos (2 heads):
[tex]\[
[2, 1, 0, 2, 2, 0, 2, 2, 3, 2, 1, 2, 1, 2, 1, 1, 2, 1, 3, 1]
\rightarrow \text{There are 9 twos}
\][/tex]
Thus, [tex]\( c = 9 \)[/tex].
- Count of threes (3 heads):
[tex]\[
[2, 1, 0, 2, 2, 0, 2, 2, 3, 2, 1, 2, 1, 2, 1, 1, 2, 1, 3, 1]
\rightarrow \text{There are 2 threes}
\][/tex]
Thus, [tex]\( d = 2 \)[/tex].
4. Filling the Frequency Table:
[tex]\[
\begin{tabular}{|c|c|}
\hline
Number of Heads & Frequency \\
\hline
0 & 2 \\
\hline
1 & 7 \\
\hline
2 & 9 \\
\hline
3 & 2 \\
\hline
\end{tabular}
\][/tex]
The completed frequency table is:
[tex]\[
a = 2, \; b = 7, \; c = 9, \; d = 2
\][/tex]
