SOLUTION: If a consumer complaint is received, what is the probability that the cause of the complaint was product appearance given that the complaint originated during the guarantee period?

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Question 1193177: If a consumer complaint is received, what is the probability that the cause of the complaint was product appearance given that the complaint originated during the guarantee period? Please help calculate the conditional probability P(A|B), where A represents the event that the cause of a particular complaint is product appearance and B represents the event that the complaint occurred during the guarantee period.
Distribution of Product Complaints
Reason for Complaint
Electrical % Mechanical % Appearance % Totals %
During Guarantee Period 18 13 32 63
After Guarantee Period 12 22 3 37
Totals 30 35 35 100
Found 2 solutions by math_tutor2020, Theo:
Answer by math_tutor2020(3820) About Me  (Show Source):
You can put this solution on YOUR website!

Given Data
Electrical%Mechanical%Appearance%Totals%
During Guarantee Period18133263
After Guarantee Period1222337
Totals303535100


A = complaint due to appearance
B = complaint happens during guarantee period

P(A | B) = P(A given B)
Since we're given event B has definitely occurred with 100% certainty, this means we focus solely on the row labeled "During Guarantee Period". Everything else is irrelevant.

We have 32% of the customers complaining about the appearance in this row, out of 63% total. We can treat these values as 32 and 63 without the percent signs.

Dividing said values gets us: 32/63 = 0.5079 = 50.79%

Answer as a fraction: 32/63
Answer in decimal form (approximate): 0.5079
Answer in percent form (approximate): 50.79%

Answer by Theo(13342) About Me  (Show Source):
You can put this solution on YOUR website!
the formula for conditional probability is:
p(A given B) = p(A and B) / p(B).
from the given data, it looks like p(B) = .63
that would mean that the probability of any type of complaint being in the guarantee period is equal to .63.
the probability of the complaint having to do with appearance and being in the guarantee period appears to be .32.
if this is correct, then p(A given B) would be equal to .32 / .63 = .5079 rounded to 4 decimal places.
i made a chart to see if this makes sense.
the chart is shown below: 

                  during          after
                  guarantee       guarantee
                  period          period             total

electrical          18%              12%               30%
mechanical          13%              22%               35%
appearance      >>> 32% <<<           3%               35%

total           >>> 63% <<<           37%              100%

from the chart, you can see that the probability that it is appearance and in the guarantee period is 32%.
you can also see that the probability that the complaint will be in the guarantee period is 63%.

p(A given B) is equal to p(A and B) / p(B).
it becomes:
p(A given B) = .32 / .63 = .5079 rounded to 4 decimal places = 50.79%.

that's what i get.