one hundred clients of a registered tax agent fall into the cayegories of personal (25 male ,30 female), corporate (10 male, 15 female) and small business (8 male, 12 female).The agent selects a client at random to begin work, find the probability that the client chosen is (a) male but not personal.
(b)personal but not male
Personnel, not personal
male but not personnel ----> 10 from corporate + 8 from small business
= 18 males
Prob(male but not personnel) = 18/(55+25+20) = 9/50
Personnel, but not male ---> females from personnel = ....
go for it.
Thanks I got it
To find the probabilities, we need to calculate the total number of clients in each category and the total number of clients in general.
Total number of clients = 100.
(a) Probability of selecting a male but not personal:
Total number of males in corporate and small business categories = 10 + 8 = 18.
Therefore, the probability of selecting a male but not personal = (number of males in corporate and small business) / (total number of clients)
= 18 / 100
= 0.18 or 18%.
(b) Probability of selecting a personal but not male:
Total number of females in personal category = 30.
Therefore, the probability of selecting a personal but not male = (number of females in personal) / (total number of clients)
= 30 / 100
= 0.3 or 30%.
To find the probability, we need to determine the total number of clients in the given categories and the number of clients that satisfy the given conditions.
(a) To find the probability that the client chosen is male but not personal, we first need to calculate the total number of male clients across the three categories. Adding the male clients in each category, we have:
Total male clients = Male personal clients + Male corporate clients + Male small business clients
Total male clients = 25 + 10 + 8 = 43
Now we need to find the number of male clients that are not in the personal category. This includes the male corporate clients and the male small business clients but excludes the male personal clients.
Number of male clients not in the personal category = Male corporate clients + Male small business clients
Number of male clients not in the personal category = 10 + 8 = 18
Finally, to find the probability, we divide the number of clients that satisfy the condition by the total number of clients:
Probability = Number of male clients not in the personal category / Total number of clients
Probability = 18 / 100
Probability = 0.18
So, the probability that the client chosen is male but not personal is 0.18 or 18%.
(b) To find the probability that the client chosen is personal but not male, we need to calculate the total number of personal clients and then subtract the number of male personal clients.
Total personal clients = Male personal clients + Female personal clients
Total personal clients = 25 + 30 = 55
Number of personal clients who are not male = Total personal clients - Male personal clients
Number of personal clients who are not male = 55 - 25 = 30
Probability = Number of personal clients who are not male / Total number of clients
Probability = 30 / 100
Probability = 0.3
So, the probability that the client chosen is personal but not male is 0.3 or 30%.