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Probability and Probability Distributions · Paper 1 — Free Maths AA HL Practice Questions

1FoundationSAQ-SBasic probability rules and conceptss5 marksPaper 1~8 min
A bag contains 55 red marbles, 33 blue marbles, and 22 green marbles. Two marbles are selected at random without replacement.
(a)
State the total number of possible outcomes when one marble is selected from the bag. [1 mark]
(b)
Calculate the probability that the first marble selected is either red or blue. [2 marks]
(c)
Given that the first marble selected is red, calculate the probability that the second marble selected is also red. [2 marks]
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Solutions

2MasterySAQ-SBasic probability rules and conceptss5 marksPaper 1~8 min
A bag contains 55 red marbles and 33 blue marbles. Two marbles are drawn at random without replacement. Let RR be the event that the first marble is red, and BB be the event that the second marble is blue.
(a)
Show that P(B)=38P(B) = \dfrac{3}{8}. [2 marks]
(b)
Find P(R∣B)P(R \mid B). [2 marks]
(c)
Determine whether RR and BB are independent events. Justify your answer. [1 mark]
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Solutions

3ChallengeSAQ-LBasic probability rules and conceptss10 marksPaper 1~15 min
A medical research team is studying a rare genetic condition. It is known that 0.5%0.5\% of the population has the condition. A diagnostic test for the condition has the following properties: - If a person has the condition, the test returns a positive result with probability 0.980.98. - If a person does not have the condition, the test returns a negative result with probability 0.950.95. The test is administered to a randomly selected person from the population.
(a)
Determine the probability that the test result is positive. [3 marks]
(b)
Determine the probability that the person has the condition, given that the test result is positive. [3 marks]
(c)
Show that the probability that the person has the condition, given that the test result is negative, is approximately 1.06×10−41.06 \times 10^{-4}. [2 marks]
(d)
A health authority proposes using this test as a mass screening tool, concluding that a positive result is strong evidence of the condition. Using your answers to parts (b) and (c), evaluate this conclusion. [2 marks]
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Solutions

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