Question

The Officer In charge at Woodlands Police Station is concerned with preserving the
Integrity of Zambia police service. It is his desire to have a female office in every team
selected for any operation. The station has nine officers in the traffic section, five of
whom are male.
i. In how many ways may a team of five consisting of at least one female officer
be selected to go on patrol? [5 marks]
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ii.	What is the probability of selecting a team of five with two female officers to go
for a surveillance operation?	[5 marks]

b) Of 100 individuals who applied for systems analyst positions with a large firm in
Lusaka, 40 had some prior work experience and 30 had professional certificate.
However, 20 of the applicants had both work experience and professional
certificate.

i.	What is the probability that a randomly chosen applicant had either work
experience or professional certificate?	[5 marks]
ii.	What is the probability that a randomly chosen applicant had a professional
certificate given that they had prior work experience?	[5 marks

Answer 1

(a) Here, there are 5 male and 4 female officers.
(i) Total no. of ways 5 members are selected from 9 officers = = 126.
No. of ways 5 members are selected so that no female officer is in the group = = 1.
No. of ways a team of five consisting of at least one female officer = 126 - 1 = 125.
(ii) No. of ways 5 members are selected so that 2 female officers are in the group = = 60.
Hence, required probability = 60/126 = 0.4762.

(b)
(i) No. of applicants who had either work experience or professional certificate = No. of applicants who had work experience + No. of applicants who had professional certificate - No. of applicants who had both work experience and professional certificate = 40 + 30 - 20 = 50.
Hence, required probability = 50/100 = 0.50.
(ii) No. of applicants who had both work experience and professional certificate = 20.
No. of applicants who had work experience = 40.
Hence, required probability = 20/40 = 0.50.