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Two made-up classes sit the same test. Class A has 30 students, and 24 of them pass…

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Try it on paper first. A hint, the key idea and the worked solution are here when you need them.

Two made-up classes sit the same test. Class A has $30$ students, and $24$ of them pass. Class B has $20$ students, and $12$ of them pass. Make the two-way table of class against result. Find the probability of a pass, given class A, and given class B. Then a student who failed is picked at random. Find the probability that the student is from class A. Give four decimal places.

Need a reminder? The key ideaShow

In a two-way table, $P(A \mid B)$ is the count of $A$ and $B$ divided by the count of $B$ : look only at the row or column of $B$ . In shares, $P(A \mid B) = \dfrac{P(A \cap B)}{P(B)}$ .

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.

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