## Exam-Style Question on Probability## A mathematics exam-style question with a worked solution that can be revealed gradually |

Question id: 363. This question is similar to one that appeared on an IB Standard paper in 2010. The use of a calculator is not allowed.

The Venn diagram below shows the events \(A\) and \(B\), and the probabilities p, q and r.

It is known that \({\rm{P}}(A) = 0.43\) , \({\rm{P}}(B) = 0.62\) and \({\rm{P}}(A \cap B) = 0.27\) .

(a) Calculate the value of p.

(b) Calculate the value of q.

(c) Calculate the value of r.

(d) Find the value of \({\rm{P}}(A|B')\)

(e) Hence, or otherwise, show that the events \(A\) and \(B\) are not independent.

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