Practice IB Mathematics Analysis and Approaches (AA) Topic SL 4.6—combined, Mutually Exclusive, Conditional, Independence, Prob Diagrams with authentic exam-style questions for both SL and HL students. This question bank focuses on the exact syllabus content for SL 4.6—combined, Mutually Exclusive, Conditional, Independence, Prob Diagrams and mirrors Paper 1, 2, 3 style where relevant.
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Find the value of .
Find the value of .
Calculate the probability that a randomly selected student participates in exactly one of these activities.
In a factory, of products are defective. Two products are selected independently at random.
Write down the probability that a product is not defective.
Find the probability that both products are not defective.
Find the probability that exactly one of the two products is defective.
Determine whether the events “first product is defective” and “second product is defective” are independent.
In a survey of employees, use public transport, use a car, and use both to commute to work. Let represent the event "uses public transport" and represent the event "uses a car".
Draw a Venn diagram to represent this information, clearly labeling all regions with the number of employees.
Find the probability that a randomly selected employee uses only one mode of transport.
In a game show, a contestant chooses one of three doors at random. The probability that a prize is behind door A is , behind door B is , and behind door C is . After choosing a door, the contestant can either stay with their choice or switch to another door. If the contestant switches, then the probability of winning is if their initial choice was door A, if their initial choice was door B, and if their initial choice was door C (so overall ).
Calculate the probability that the contestant wins if they stay with their initial choice.
Determine whether the events "choosing door A" and "winning by switching" are independent.
In a factory, of products are defective. Two products are selected at random and the defect status of each product is independent of the other.
Write down the probability that a product is not defective.
Find the probability that both products are not defective.
Find the probability that exactly one of the two products is defective.
Determine whether the events “first product is defective” and “second product is defective” are independent.