1) One hundred clients of a registered tax agent fall into the categories of personal (25 male, 30 female), corporate (10 male, 15 female) and small business (8 male, 12 female). The agent selects one of the clients at random to begin work. Find the probability that the client chosen is:
(a) male (b) female (c) personal (d) corporate (e) small business
Total number of males
=25+10+8=43
Total number of clients
= 100
Selection is random.
=>
Probability, P(M)
= 43/100
= 0.43
You can proceed with the remaining questions in the same manner.
really helpful
To find the probability, we need to know the total number of clients and the number of clients in each category.
Let's break down the information given:
- Total number of clients: 100
- Gender breakdown:
- Personal: 25 male, 30 female
- Corporate: 10 male, 15 female
- Small business: 8 male, 12 female
Now let's solve each part of the question:
(a) Probability that the client chosen is male:
To find the probability, we need to divide the number of male clients by the total number of clients.
Number of male clients: 25 (personal) + 10 (corporate) + 8 (small business) = 43
Probability = Number of male clients / Total number of clients
Probability = 43 / 100
(b) Probability that the client chosen is female:
To find the probability, we need to divide the number of female clients by the total number of clients.
Number of female clients: 30 (personal) + 15 (corporate) + 12 (small business) = 57
Probability = Number of female clients / Total number of clients
Probability = 57 / 100
(c) Probability that the client chosen falls into the personal category:
To find the probability, we need to divide the number of clients in the personal category by the total number of clients.
Number of clients in personal category: 25 (male) + 30 (female) = 55
Probability = Number of personal clients / Total number of clients
Probability = 55 / 100
(d) Probability that the client chosen falls into the corporate category:
To find the probability, we need to divide the number of clients in the corporate category by the total number of clients.
Number of clients in corporate category: 10 (male) + 15 (female) = 25
Probability = Number of corporate clients / Total number of clients
Probability = 25 / 100
(e) Probability that the client chosen falls into the small business category:
To find the probability, we need to divide the number of clients in the small business category by the total number of clients.
Number of clients in small business category: 8 (male) + 12 (female) = 20
Probability = Number of small business clients / Total number of clients
Probability = 20 / 100
Now you can calculate the probabilities for each part.