A school's lower sixth intake is 55% from its own O-level pupils and 45% from other schools. Of those who did O-level elsewhere, 90% pass A-level; of those who did O-level at the school, 70% pass. A recent A-level graduate is selected at random. What is the probability that this pupil passed A-level?

A0.385

B0.405

C0.79

D0.81

Explanation

By the law of total probability,

P(\text{pass}) = P(\text{pass}|\text{school})P(\text{school}) + P(\text{pass}|\text{other})P(\text{other}) = 0.70\times0.55 + 0.90\times0.45 = 0.385+0.405 = 0.79

Derived from ZIMSEC Maths Paper 1, November 2008, Q2 (Statistics)

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