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Independent and Dependent Events — Free MYP5 Mathematics (Extended) Practice Questions
1QuestionUsing Probability Trees for Multi-Stage EventsConcept Practice
3 marks~5 minCriterion A
A school supplies coordinator tracks how students choose writing tools. Based on purchasing records, the probability that a student selects a pen is and a pencil is . Given a pen is chosen, the probability of selecting a blue refill is and a black refill is . Given a pencil is chosen, the probability of selecting a blue refill is and a black refill is .
a
Calculate the probability that a randomly selected student chooses a blue refill. [2]
b
The coordinator orders blue refills for exactly half of all students. Advise the coordinator whether this order quantity is appropriate, justifying your answer using your result from part (a). [1]
Solutions
2QuestionReal-Life Applications Games Genetics and Decision-MakingAssessment Practice
2 marks~3 minCriterion C
In genetic counselling, both parents are confirmed carriers of a recessive disorder. The probability that any one child inherits the disorder is .
Explain why the assumption of independent assortment is necessary to calculate the probability that two children both inherit the disorder, and identify one limitation of this assumption in real genetic contexts. [2]
Explain why the assumption of independent assortment is necessary to calculate the probability that two children both inherit the disorder, and identify one limitation of this assumption in real genetic contexts. [2]
Solutions
3QuestionUsing Probability Trees for Multi-Stage EventsAssessment Practice
7 marks~11 minCriterion B
A quality-control engineer tests microchips by running them through a sequence of independent diagnostic checks. At each check, a chip either passes (P) or fails (F), each with equal probability.
a
Write down the number of distinct outcomes after 1 check, after 2 checks, and after 3 checks. Identify the pattern in your sequence. [2]
b
Deduce a formula for the total number of distinct outcomes after checks, each with equally likely results. Justify your formula using the structure of a probability tree. [2]
c
The engineer runs 4 checks on each chip. Construct a probability tree for this 4-stage process and use your formula to verify the total number of distinct paths. A chip is accepted only if it passes all 4 checks. Advise the engineer whether this acceptance criterion is suitable for a production line, justifying your answer using probability. [3]
Solutions
4QuestionUsing Probability Trees for Multi-Stage EventsAssessment Practice
10 marks~15 minCriterion D
A hospital uses a rapid antigen test to screen for a disease with a prevalence of 2%. The test has a sensitivity of 90% — the probability of a positive result given the disease is present — and a specificity of 95% — the probability of a negative result given the disease is absent.
a
Construct a probability tree diagram for two stages: disease status (has disease / no disease) and test result (positive / negative). Clearly label all branches with their probabilities. [3]
b
Using your tree, calculate the probability that a randomly selected individual tests positive. [2]
c
Calculate the positive predictive value (PPV): the probability that an individual actually has the disease given a positive test result. [2]
d
The disease prevalence rises to 10% during an outbreak and falls to 0.5% in a low season. Calculate the PPV in each case, then advise the hospital whether the test is suitable as a standalone screening tool across all three prevalence levels, justifying your recommendation with reference to false positive and false negative consequences and the limitations of this model. [3]
Solutions
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