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For reporting purposes, he would like to find the probability that a randomly selected employee
(or an employee that is to be hired in the future) is high risk or will file a mental health claim. As
he is writing his report, he reaches a speed bump:
Letting ,
( ) ( ) ( )
He quickly realizes that this probability is invalid because a probability cannot be greater than 1,
or 100%. What happened
SOLUTION:
We first organize his data into a table to help us better see what is happening:
Claim\Risk Low High
Physical .20
Mental .70
.40
The probabilities outside of the boxes represent totals for mental health claims and for high risk
claims. The probability in the 1-1 entry of the table represents the probability of being low risk
and filing a physical health claim. Since we know that this data represents all of those who have
filed claims, we know that 100% have filed one type or the other. Additionally, each employee
considered falls into one of the two risk categories. So we fill in more details:
Claim\Risk Low High
Physical .20 .30
Mental .70
.60 .40
We can also proceed to fill in the boxes in the table, since each person falls into exactly one of
the four positions (low physical, low mental, high physical, high mental):
Claim\Risk Low High
Physical .20 .10 .30
Mental .40 .30 .70
.60 .40
Now, the analyst added to second row total with the second column total, as highlighted in the
table below:
Claim\Risk Low High
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