IOP2601 ASSIGNEMNT 2 SEMESTER 2 2024

IOP2601 ASSIGNMENT 2 SEMESTER 2 2024




IOP2601 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