Conditional probability from a distribution

Practise conditional probability from a distribution with an original VectorPaths question, worked explanation and related VCE Methods practice.

3 practice marks

Original practice question

A random variable has $P(X=0)=1/5$, $P(X=1)=3/10$, $P(X=2)=2/5$ and $P(X=3)=1/10$. (a) Find $P(X\geq1)$. [1 marks] (b) Find $P(X\geq2\mid X\geq1)$. [2 marks]

Worked explanation

• Part (a)

  Use the complement: $P(X\geq1)=1-P(X=0)=1-1/5=4/5$.

• Part (b)

  The intersection is $X\geq2$, of probability $2/5+1/10=1/2$. Divide by the condition probability: $(1/2)/(4/5)=5/8$.

(a) $4/5$.; (b) $5/8$.

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