MediumMathematicsHigh School (11–12)Statistics and Probability › Conditional Probability and Bayes' TheoremNumericalBoard ExamSATAPA-LevelIBAEEE (Amrita)
A transport office surveys 200 commuters…
Contributed by StemPy LabTry it on paper first. A hint, the key idea and the worked solution are here when you need them.
A transport office surveys commuters. Of them, are men and are women. Altogether commuters travel by train, and of the train travellers are women. One commuter is chosen at random from the survey. Find the probability that the commuter is a woman, given that the commuter travels by train. Then find the probability that the commuter travels by train, given that the commuter is a woman. Finally find the probability of travelling by train, given that the commuter is a man. Give decimals to four places.
Need a reminder? The key ideaShow
Once is given, the sample space is . So , which is when the outcomes are equally likely. Divide by the event after the bar.
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. Woman given train. The group is the train travellers. Of them, are women. So the probability is .
Step 2. Train given woman. The group is the women. Of them, travel by train. So the probability is .
Step 3. Train given man. Men on the train: . The group is the men. The probability is .
Answer: , and .
Watch out. The first two answers look alike, but they answer different questions. One divides by and the other by .
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