EasyMathematicsHigh School (11–12)Statistics and Probability › Conditional Probability and Bayes' TheoremNumericalBoard ExamAPA-LevelIB
Karan travels to work by bus with probability 0.6 and by tram with probability 0.4…
Contributed by StemPy LabTry it on paper first. A hint, the key idea and the worked solution are here when you need them.
Karan travels to work by bus with probability and by tram with probability . The bus is late with probability , and the tram is late with probability . On a random morning, find four probabilities. Find the probability that he goes by bus and is late, and the probability that he goes by tram and is late. Then find the probability that he is late, and the probability that he is on time.
Need a reminder? The key ideaShow
For a partition , the law of total probability is . Multiply along every path that ends in , then add the paths. The cases must not overlap and must cover everything.
The worked solution
Have you tried it?
Work it out on paper first. It is fine to get stuck or make a mistake: that is how we learn. When you are ready, go through the solution one step at a time, and check each step against your own.
Step 1. The bus path. .
Step 2. The tram path. .
Step 3. Late. The two paths do not overlap, so .
Step 4. On time. .
Answer: , , and .
Check. The overall chance of being late, , lies between the two rates and , and nearer because the bus is used more often.
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