,MIP2602 Assignment 4 Memo | Due 15 August
2025. Step by Step Calculations provided.
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)
1.2 One letter is selected at random from the word STATISTICS.
What is the probability that the letter is:
1.2.1 S (2) 1.2.2 E (2) 1.2.3 T or C (3)
1.3 A jar contains 4 red, 5 yellow, and 6 blue marbles. Two
marbles are drawn one after the other with replacement.
Determine the probability that:
1.3.1 Neither marble is red. (2) 1.3.2 The first is blue and the
second is yellow. (2) 1.3.3 Both are yellow. (1)
1.4 Two fair dice (one white, one red) are rolled simultaneously.
The total of the two faces is recorded. What is the probability
that: 1.4.1 The total is 9. (2) 1.4.2 The total is less than 5. (2)
1.4.3 The total is greater than or equal to 10. (2)
1.5 The table below shows the qualifications of 120 hospital
staff across departments.
1.5.1 What is the probability that a randomly selected staff
member: 1.5.1.1 Works in the surgery department, given they
have a degree (3) 1.5.1.2 Has either a diploma or works in the
admin department (3)
, 1.5.2 Which qualification level appears to be most common
among staff in the Surgery department? Support your answer
with numbers. (2)
1.5.3 What might the data suggest about the qualification
trends in the admin department compared to the ER? (2)
1.6 Using information in 1.5, draw a probability tree diagram to
represent the process of randomly selecting a staff member
from the hospital, identifying their department, and
determining their qualification level. (12)
(It is acceptable to start with either the department or
qualification but ensure that the branches are accurate.)
1.7 Use the tree diagram you drew in 1.6 to answer the
following question:
1.7.1 Which combination has the highest joint probability of
selection? Explain why. (2)
1.7.2 Suppose the hospital is planning a training programme for
diploma holders. Which department should they prioritize, and
why? (2)
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____________________________________________________
_____________________________________
2025. Step by Step Calculations provided.
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)
1.2 One letter is selected at random from the word STATISTICS.
What is the probability that the letter is:
1.2.1 S (2) 1.2.2 E (2) 1.2.3 T or C (3)
1.3 A jar contains 4 red, 5 yellow, and 6 blue marbles. Two
marbles are drawn one after the other with replacement.
Determine the probability that:
1.3.1 Neither marble is red. (2) 1.3.2 The first is blue and the
second is yellow. (2) 1.3.3 Both are yellow. (1)
1.4 Two fair dice (one white, one red) are rolled simultaneously.
The total of the two faces is recorded. What is the probability
that: 1.4.1 The total is 9. (2) 1.4.2 The total is less than 5. (2)
1.4.3 The total is greater than or equal to 10. (2)
1.5 The table below shows the qualifications of 120 hospital
staff across departments.
1.5.1 What is the probability that a randomly selected staff
member: 1.5.1.1 Works in the surgery department, given they
have a degree (3) 1.5.1.2 Has either a diploma or works in the
admin department (3)
, 1.5.2 Which qualification level appears to be most common
among staff in the Surgery department? Support your answer
with numbers. (2)
1.5.3 What might the data suggest about the qualification
trends in the admin department compared to the ER? (2)
1.6 Using information in 1.5, draw a probability tree diagram to
represent the process of randomly selecting a staff member
from the hospital, identifying their department, and
determining their qualification level. (12)
(It is acceptable to start with either the department or
qualification but ensure that the branches are accurate.)
1.7 Use the tree diagram you drew in 1.6 to answer the
following question:
1.7.1 Which combination has the highest joint probability of
selection? Explain why. (2)
1.7.2 Suppose the hospital is planning a training programme for
diploma holders. Which department should they prioritize, and
why? (2)
[59]
____________________________________________________
_____________________________________
