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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]\[ a = \square \][/tex]

[tex]\[ b = \square \][/tex]

[tex]\[ c = \square \][/tex]

[tex]\[ d = \square \][/tex]

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

Sagot :

GinnyAnsweridn
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]
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