Exam-Style Problem

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June 2012 p61 q2
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Maria has 3 pre-set stations on her radio. When she switches her radio on, there is a probability of 0.3 that it will be set to station 1, a probability of 0.45 that it will be set to station 2 and a probability of 0.25 that it will be set to station 3. On station 1 the probability that the presenter is male is 0.1, on station 2 the probability that the presenter is male is 0.85 and on station 3 the probability that the presenter is male is \(p\). When Maria switches on the radio, the probability that it is set to station 3 and the presenter is male is 0.075.

  1. Show that the value of \(p\) is 0.3.
  2. Given that Maria switches on and hears a male presenter, find the probability that the radio was set to station 2.
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