Add the frequency to the table. The frequency of the unmentioned letters will be the difference of the total of the frequencies, 100, and the sum of the frequencies of listed letters.
Letter
a
e
i
n
o
r
s
t
Others
Frequency
8
14
7
6
8
4
6
9
38
Probability
0.08
0.14
0.07
0.06
0.08
0.04
0.06
0.09
0.38
Practice makes perfect
A student chose 100 letters at random from a page of a textbook. Partial results are given in a table. We want to make a probability distribution for this data. Let's rearrange the table a bit. We will add a row Frequency that will represent the count for particular letters.
Letter
a
e
i
n
o
r
s
t
Tally
|||| |||
|||| |||| ||||
|||| ||
|||| |
|||| |||
||||
|||| |
|||| ||||
Frequency
8
14
7
6
8
4
6
9
Note that these are just partial results. To take every possible result into consideration we will add a category for not mentioned letters. We will mark them as others. Their frequency will be the difference between the total frequency, 100, and the sum of the given frequencies. Let's calculate it!
The frequency of other letters is 38. Now we can add the category Others to our table. Note that since we have the row Frequency we can now skip the row Tally, because they represent the same thing.
Letter
a
e
i
n
o
r
s
t
Others
Frequency
8
14
7
6
8
4
6
9
38
Finally we can find the probability distribution for these data. To do so we will calculate the relative frequencies for every category in the table. The relative frequency is the quotient of the frequency of a particular event and the total of the frequencies — in our case, 100. The relative frequency represents the probability of selecting a particular letter.
Letter
a
e
i
n
o
r
s
t
Others
Frequency
8
14
7
6
8
4
6
9
38
Probability
8/100=0.08
14/100=0.14
7/100=0.07
6/100=0.06
8/100=0.08
4/100=0.04
6/100=0.06
9/100=0.09
38/100=0.38
The table shows the probability distribution for the given data.
