Question 2203

The events ${A,B}$ and ${C}$ are such that ${P(A)=a,} \allowbreak {P(B)=b}$ and ${P(C)=c.}$

It is also given that events ${A}$ and ${B}$ are independent, and that events ${A}$ and ${C}$ are mutually exclusive.

(2 marks) (a) Find an expression for

{P\left(A\cap B'\right)}

and hence prove that

{A}

and

{B'}

are independent events.

It is now given that ${P(A)=\frac{1}{5},} \allowbreak {P(B \cap C)=\frac{4}{25}}$ and ${{P(A' \cap B' \cap C')=\frac{2}{25}}}$

(4 marks) (b) Find the greatest and least possible value of

{P(A\cap B).}

This question is inspired by the 2010 A Levels H2 Mathematics Paper 2 Question 7.

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Solution