Question

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

2, 1, 0, 2, 2, 0, 2, 2, 3, 2, 1, 2, 1, 2, 1, 1, 2, 1, 3, 1

complete the frequency table.

\\(a = \\) , \\(b = \\) , \\(c = \\) ,
\\(d = \\)

Explanation:

Count occurrences of each value

The given data set of 20 trials is:

$$ 2, 1, 0, 2, 2, 0, 2, 2, 3, 2, 1, 2, 1, 2, 1, 1, 2, 1, 3, 1 $$

• Count of \(0\):

There are 2 occurrences of \(0\) (at positions 3 and 6).

$$ a = 2 $$

• Count of \(1\):

There are 7 occurrences of \(1\) (at positions 2, 11, 13, 15, 16, 18, 20).

$$ b = 7 $$

• Count of \(2\):

There are 9 occurrences of \(2\) (at positions 1, 4, 5, 7, 8, 10, 12, 14, 17).

$$ c = 9 $$

• Count of \(3\):

There are 2 occurrences of \(3\) (at positions 9, 19).

$$ d = 2 $$

Verify total count

Sum the frequencies to ensure they equal the total number of trials (20):

$$ a + b + c + d = 2 + 7 + 9 + 2 = 20 $$

The counts are correct.

Answer:

Complete the frequency table.

\(a =\) <blank>2</blank>, \(b =\) <blank>7</blank>, \(c =\) <blank>9</blank>, \(d =\) <blank>2</blank>.