Independent and Dependent Events
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Independent and Dependent Events — Free MYP5 Mathematics (Standard) Practice Questions

1QuestionReal-Life Applications Games Genetics and Decision-MakingAssessment Practice
4 marks~6 minCriterion C
A genetics laboratory crosses two pea plants and records the phenotypes of 80 offspring.

Tall with green seeds: 30
Tall with yellow seeds: 20
Short with green seeds: 10
Short with yellow seeds: 20
a
Calculate the conditional probability that a randomly selected offspring is tall, given that it has green seeds. [2]
b
A second laboratory claims that height and seed colour are independent traits in this cross. Justify whether the data support this claim. [2]
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2QuestionUsing Probability Trees for Multi-Stage EventsAssessment Practice
4 marks~6 minCriterion A
A quality-control engineer randomly selects one of two biased coins from a box. Coin A has P(H)=0.6P(\text{H}) = 0.6 and Coin B has P(H)=0.3P(\text{H}) = 0.3, with P(Coin A)=0.4P(\text{Coin A}) = 0.4 and P(Coin B)=0.6P(\text{Coin B}) = 0.6. The selected coin is flipped twice. A partially completed probability tree shows the coin selection and first-flip outcomes.
a
Construct the second-flip branches on the tree diagram. [1]
b
Calculate P(H on first flip)P(\text{H on first flip}) and P(HH)P(\text{HH}). [2]
c
The sensor flags a fault only when the second flip is Heads given the first was also Heads. Find P(H on second flip∣H on first flip)P(\text{H on second flip} \mid \text{H on first flip}) and advise the engineer whether this fault signal is reliable enough to act on without further testing. [1]
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3QuestionUsing Probability Trees for Multi-Stage EventsAssessment Practice
7 marks~11 minCriterion D
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 nn checks, each with mm 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]
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4QuestionConditional Probability IntroductoryAssessment Practice
8 marks~12 minCriterion B
A quality-control technician samples marbles from a production batch. A bag contains red and blue marbles totalling 10. Four compositions are tested by drawing two marbles without replacement.

Initial composition (R,B)(R, B):
Trial 1: (4,6)(4, 6) — Trial 2: (5,5)(5, 5) — Trial 3: (6,4)(6, 4) — Trial 4: (7,3)(7, 3)
a
Calculate P(second blue∣first red)P(\text{second blue} \mid \text{first red}) for each trial. [2]
b
Deduce the general formula for P(second blue∣first red)P(\text{second blue} \mid \text{first red}) in terms of RR and BB, showing your reasoning. [2]
c
A new batch has 10 red and 2 blue marbles. The technician's acceptance criterion requires P(second blue∣first red)>0.20P(\text{second blue} \mid \text{first red}) > 0.20. Calculate the probability and advise the technician whether this batch should be accepted or rejected, justifying your answer in context. [4]

Solutions

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