MIP2602 Assignment 4
(COMPLETE ANSWERS)
2025 - DUE 15 August
2025
For more assistance contact:
DISTINCTION GUARANTEED
, MIP2602 Assignment 4 (COMPLETE ANSWERS) 2025 -
DUE 15 August 2025
SECTION A: PROBABILITY QUESTION 1 1.1 A bag contains a total of 10 marbles: 3
red marbles, 4 blue marbles, 2 green marbles, and 1 yellow marble. 1.1.1 If one
marble is randomly drawn from the bag, what is the theoretical probability of
drawing: 1.1.1.1 A red marble = ____________ 1.1.1.2 A blue marble = ____________
1.1.1.3 A green marble = ____________ 1.1.1.4 A yellow marble = ____________ (4)
1.1.2 Conduct an experiment where you draw one marble at a time from the bag
and record the colour, returning it each time. Repeat this 14 times. Use the table
below to track your results: (7) 1.1.3 Based on the results you found in question
1.1.2, calculate the experimental probability for each colour: 1.1.3.1 P(Red) =
____________ 1.1.3.2 P(Blue) = ____________ 1.1.3.3 P(Green) = ____________ 1.1.3.4
P(Yellow) = ____________ (4) 1.1.4 How do the theoretical and experimental
probabilities compare in your results? Mention one reason why they might be
different. (2)
Nice — let’s do this step-by-step.
1.1.1 Theoretical probabilities (one draw from 10 marbles)
1.1.1.1 A red marble = 3/10
1.1.1.2 A blue marble = 4/10 = 2/5
1.1.1.3 A green marble = 2/10 = 1/5
1.1.1.4 A yellow marble = 1/10
1.1.2 & 1.1.3 — Experiment (14 draws with replacement)
I can’t physically draw marbles for you, so I ran a reproducible example simulation of 14 draws with replacement and
showed the sequence and counts for you to copy into your table (you’ll see two tables from the simulation: the sequence
of 14 draws and the counts/probabilities).
Example (from the 14 simulated draws):
Sequence of draws (example): Blue, Red, Red, Red, Green, Blue, Green, Red, Blue, Red, Red, Blue, Red, Red.
Counts from that example: Red = 8, Blue = 4, Green = 2, Yellow = 0.
So the experimental probabilities from that example (counts ÷ 14):
1.1.3.1 P(Red) = 8/14 ≈ 0.571
1.1.3.2 P(Blue) = 4/14 ≈ 0.286
1.1.3.3 P(Green) = 2/14 ≈ 0.143
1.1.3.4 P(Yellow) = 0/14 = 0.000
(If you do the physical experiment yourself, just fill your table with the 14 results and compute each experimental
probability as count/14.)
1.1.4 Compare theoretical vs experimental & one reason for difference (short answer)
(COMPLETE ANSWERS)
2025 - DUE 15 August
2025
For more assistance contact:
DISTINCTION GUARANTEED
, MIP2602 Assignment 4 (COMPLETE ANSWERS) 2025 -
DUE 15 August 2025
SECTION A: PROBABILITY QUESTION 1 1.1 A bag contains a total of 10 marbles: 3
red marbles, 4 blue marbles, 2 green marbles, and 1 yellow marble. 1.1.1 If one
marble is randomly drawn from the bag, what is the theoretical probability of
drawing: 1.1.1.1 A red marble = ____________ 1.1.1.2 A blue marble = ____________
1.1.1.3 A green marble = ____________ 1.1.1.4 A yellow marble = ____________ (4)
1.1.2 Conduct an experiment where you draw one marble at a time from the bag
and record the colour, returning it each time. Repeat this 14 times. Use the table
below to track your results: (7) 1.1.3 Based on the results you found in question
1.1.2, calculate the experimental probability for each colour: 1.1.3.1 P(Red) =
____________ 1.1.3.2 P(Blue) = ____________ 1.1.3.3 P(Green) = ____________ 1.1.3.4
P(Yellow) = ____________ (4) 1.1.4 How do the theoretical and experimental
probabilities compare in your results? Mention one reason why they might be
different. (2)
Nice — let’s do this step-by-step.
1.1.1 Theoretical probabilities (one draw from 10 marbles)
1.1.1.1 A red marble = 3/10
1.1.1.2 A blue marble = 4/10 = 2/5
1.1.1.3 A green marble = 2/10 = 1/5
1.1.1.4 A yellow marble = 1/10
1.1.2 & 1.1.3 — Experiment (14 draws with replacement)
I can’t physically draw marbles for you, so I ran a reproducible example simulation of 14 draws with replacement and
showed the sequence and counts for you to copy into your table (you’ll see two tables from the simulation: the sequence
of 14 draws and the counts/probabilities).
Example (from the 14 simulated draws):
Sequence of draws (example): Blue, Red, Red, Red, Green, Blue, Green, Red, Blue, Red, Red, Blue, Red, Red.
Counts from that example: Red = 8, Blue = 4, Green = 2, Yellow = 0.
So the experimental probabilities from that example (counts ÷ 14):
1.1.3.1 P(Red) = 8/14 ≈ 0.571
1.1.3.2 P(Blue) = 4/14 ≈ 0.286
1.1.3.3 P(Green) = 2/14 ≈ 0.143
1.1.3.4 P(Yellow) = 0/14 = 0.000
(If you do the physical experiment yourself, just fill your table with the 14 results and compute each experimental
probability as count/14.)
1.1.4 Compare theoretical vs experimental & one reason for difference (short answer)
