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IOP2601 ASSIGNEMNT 2 SEMESTER 2 2024
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IOP2601 ASSIGNMENT 2 SEMESTER 2 2024IOP2601 ASSIGNMENT 2 SEM 2 2024 GUIDE IS A PRODUCT OF INTERNAL AND
EXTERNAL RESEARCH THAT INCLUDES THE STUDY GUIDE, PRESCRIBED
TEXTBOOK, AND OTHER AUTHENTIC SOURCES.
, IOP2601 ASSIGNMENT 2 SEMESTER 2 2024
Question 1: Probability Calculation (11 marks)
This question involves determining the probabilities associated with Sonia and Jack winning
the Volunteer of the Year award. Below are the solutions:
1. Probability that Sonia will win first prize
Total nominations = 200
Sonia's nominations = 40
𝑆𝑜𝑛𝑖𝑎′ 𝑠 𝑛𝑜𝑚𝑖𝑛𝑎𝑡𝑖𝑜𝑛𝑠
Probability = 𝑇𝑜𝑡𝑎𝑙 𝑛𝑜𝑚𝑖𝑛𝑎𝑡𝑖𝑜𝑛𝑠
40
P(Sonia wins) = 200 = 0.20
2. Probability that Jack will win first prize
Jack's nominations = 20
Probability = 𝐽𝑎𝑐𝑘′𝑠 𝑛𝑜𝑚𝑖𝑛𝑎𝑡𝑖𝑜𝑛𝑠 / 𝑇𝑜𝑡𝑎𝑙 𝑛𝑜𝑚𝑖𝑛𝑎𝑡𝑖𝑜𝑛𝑠
P (Jack wins) = 20/200 = 0.10
3. If Sonia wins first prize, what is the probability that Jack will win second prize?
After Sonia wins, 200 - 40 = 160 nominations remain.
P (Jack wins second) = 20/160 = 0.125
4. If Jack wins first prize, what is the probability that Sonia will win the second
prize?
After Jack wins, 200 - 20 = 180 nominations remain.
P (Sonia wins second) = 40/180 = 0.22
5. Probability that Sonia and Jack will win first and second prize respectively
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