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IOP2601 Assignment 2 (COMPLETE ANSWERS) Semester 2 2024 - DUE 26 August 2024
IOP2601 Assignment 2 (COMPLETE ANSWERS) Semester 2 2024 - DUE 26 August 2024
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I,OP2601 Assignment 2 (COMPLETE ANSWERS) Semes
ter 2 2024 - DUE 26 August 2024 ; 100% T
RUSTED Comple
QUESTION 1 [11] Use the information below to answer the
questions that follow. A local community centre will soon be
celebrating its annual "Volunteer of the Year" award, with the
winner receiving a R20 000 gift card and a certificate of
appreciation. Two volunteers, Sonia and Jack, are finalists for
this prize. Sonia has been volunteering at the centre for fifteen
(15) years and is recognised for her dedication and vast
contributions. She received 40 nominations from various
community members. Jack is a new volunteer who has made a
big impact with his energy and innovative ideas. He received 20
nominations from both community members and employees.
The community centre's administration received 200 valid
nominations. Sonia and Jack are now excitedly anticipating the
announcement of the winner, conscious that their chances are
determined by the number of nominations they received, as
well as the selection committee's considerations. 1.1 What is
the probability that Sonia will win first prize? (2) 1.2 What is the
possibility that Jack will win first prize? (2) 1.3 If Sonia wins first
prize, what is the probability that Jack will win second prize?
(The person winning the first prize is not eligible to be selected
for the second or third prize). (2) 1.4 If Jack wins the first prize,
what is the probability that Sonia will win the second prize?
(The person winning the first prize is not eligible to be selected
, for the second or third prize). (2) 1.5 What is the probability
that Sonia and Jack will win first and second prize, respectively?
1.1 What is the probability that Sonia will win first prize? (2
marks)
Sonia received 40 nominations out of 200 valid
nominations.
The probability P(Sonia wins)P(Sonia \ wins)P(Sonia wins)
is calculated as:
P(Sonia wins)=Number of nominations for SoniaTotal number of
nominations=40200=0.2P(Sonia \ wins) = \frac{\text{Number of
nominations for Sonia}}{\text{Total number of nominations}} = \
frac{40}{200} =
0.2P(Sonia wins)=Total number of nominationsNumber of nomi
nations for Sonia=20040=0.2
Answer:
P(Sonia wins)=0.2P(Sonia \ wins) = 0.2P(Sonia wins)=0.2
1.2 What is the probability that Jack will win first prize? (2
marks)
Jack received 20 nominations out of 200 valid nominations.
The probability P(Jack wins)P(Jack \ wins)P(Jack wins) is
calculated as:
P(Jack wins)=Number of nominations for JackTotal number of n
ominations=20200=0.1P(Jack \ wins) = \frac{\text{Number of
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