IB Maths AI SL 4.6 Combined Conditional and Independent Events Topic Practice

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Study SL 4.6—Combined, conditional and independent events conceptsOpen the corresponding Concept lesson for explanations, examples and exam connections.

Question 1

[Maximum number: 9]

A large international sports tournament tests their athletes for banned substances.
They interpret a positive test result as meaning that the athlete uses banned substances. A negative result means that they do not.
The probability that an athlete uses banned substances is estimated to be 0.06 .
If an athlete uses banned substances, the probability that they will test positive is 0.71 .
If an athlete does not use banned substances, the probability that they will test negative is 0.98 .

Question (a)

(a)

Using the information given, copy (into your answer booklet) and complete the following tree diagram.

Figure for Question (a) — IB Maths AI SL
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Question (b)

(b)

Determine the probability that a randomly selected athlete does not use banned substances and tests negative.

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Question (c)

(c)

If two athletes are selected at random, calculate the probability that both athletes do not use banned substances and both test negative.

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Question (d)

(d)

Calculate the probability that a randomly selected athlete will receive an incorrect test result.

[ 3 ]
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