Conditional probability from a continuous density

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

4 practice marks

Original practice question

X has density $f(x)=2x$ for $0\leq x\leq1$, and zero elsewhere. (a) Find $P(X>1/2)$. [2 marks] (b) Find $P(X>3/4\mid X>1/2)$. [2 marks]

Worked explanation

• Part (a)

  $P(X>1/2)=\int_{1/2}^1 2x\,dx=1-1/4=3/4$.

• Part (b)

  The numerator is $P(X>3/4)=1-9/16=7/16$. Divide by $3/4$ to obtain $7/12$.

(a) $3/4$.; (b) $7/12$.

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