To solve this problem, we need to count the frequency of each number of heads that appeared when flipping the 3 coins 20 times.
We have the following data for the number of heads:
[tex]\[ 2, 1, 0, 2, 2, 0, 2, 2, 3, 2, 1, 2, 1, 2, 1, 1, 2, 1, 3, 1 \][/tex]
Let’s break it down step by step:
### Step 1: Count the number of times 0 heads appeared
To determine the value of [tex]\( a \)[/tex]:
- We see that 0 heads appeared twice (3rd and 6th positions).
So, [tex]\( a = 2 \)[/tex].
### Step 2: Count the number of times 1 head appeared
To determine the value of [tex]\( b \)[/tex]:
- We see that 1 head appeared seven times (2nd, 11th, 13th, 15th, 16th, 17th, and 20th positions).
So, [tex]\( b = 7 \)[/tex].
### Step 3: Count the number of times 2 heads appeared
To determine the value of [tex]\( c \)[/tex]:
- We see that 2 heads appeared nine times (1st, 4th, 5th, 7th, 8th, 10th, 12th, 14th, and 18th positions).
So, [tex]\( c = 9 \)[/tex].
### Step 4: Count the number of times 3 heads appeared
To determine the value of [tex]\( d \)[/tex]:
- We see that 3 heads appeared twice (9th and 19th positions).
So, [tex]\( d = 2 \)[/tex].
Now, we can complete the frequency table as follows:
[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]
