Elisa S. answered • 3d
Experienced Math Tutor & Adjunct Professor Helping Students Build
Question 1: The probability that a customer is either a business with annual sales of $100K or less OR utilizes Tier 5 services
a) Because the customer is in one group or another group, we can use the addition rule for two events:
P(A or B) = P(A)+ P(B) - P(A and B)
Let's define the events:
A = customer has annual sales of $100K or less
B = customer utilizes Tier 5 services
Using the table, we can find A and B.
A = 123 + 45+ 2 + 0 + 0 = 170
B = 0 + 0 + 0 + 0 + 37 = 37
and how many customers who are both A and B which is zero because the two events do not overlap.
b) Let's figure out the probability!
P(A) = 170/2577
P(B) = 37/2577
P(A and B) = 0/2577
P( A or B) = 170/2577 + 37/2577 - 0/2577
P(A or B) = 207/2577 =0.0803 ~.0803
Therefore, the probability is 8.03%
Question 2: The Probability that a customer with annual sales between $1M and $5M utilizes Tier 3 services
a) Because the question asks for the probability that a customer uses Tier 3 services given that the customer has annual sales between $1M and $5M, this is a conditional probability or P(B|A)
where
A = customers that have annual sales between $1M and $5M
B = customer utilizes Tier 3 services
c) Now, let's convert the data to probabilities using relative frequency
A = 42 + 127 + 344 + 186 + 0 = 699
and customers with annual sales between $1M and $5M who use Tier 3: 344
Therefore, P(A) = 699/2577
P(A and B) = 344/2577
d) Using conditional probability to get the final answer.
P(B|A) = P(A and B)/P(A) = (344/2577) / (699/2577) = 344/699 =0.492 ~.4921
Therefore, the probability is 49.21%.
