Practise IB Mathematics SL/HL 4.6 by applying combined, conditional and independent events methods to questions from the Question Bank.
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 .
Using the information given, copy (into your answer booklet) and complete the following tree diagram.
Determine the probability that a randomly selected athlete does not use banned substances and tests negative.
If two athletes are selected at random, calculate the probability that both athletes do not use banned substances and both test negative.
Calculate the probability that a randomly selected athlete will receive an incorrect test result.