Union, complement and independence

Practise union, complement and independence with an original VectorPaths question, worked explanation and related VCE Methods practice.

3 practice marks

Original practice question

Events A and B satisfy $P(A)=3/5$, $P(B)=1/2$ and $P(A\cap B)=1/5$. (a) Find $P(A\cup B)$ and the probability of neither event. [2 marks] (b) Determine whether A and B are independent, with a reason. [1 marks]

Worked explanation

• Part (a)

  $P(A\cup B)=3/5+1/2-1/5=9/10$. The complement has probability $1-9/10=1/10$.

• Part (b)

  $P(A)P(B)=(3/5)(1/2)=3/10\ne1/5=P(A\cap B)$.

(a) $9/10$ and $1/10$.; (b) They are not independent.

Original VectorPaths practice; not an official VCAA question or marking rubric.