Binomial exact count and complement

Practise binomial exact count and complement with an original VectorPaths question, worked explanation and related VCE Methods practice.

4 practice marks

Original practice question

Each of 5 independent components works with probability $2/5$. Let X be the number that work. (a) Find $P(X=2)$ exactly. [2 marks] (b) Find $P(X\geq1)$ exactly. [2 marks]

Worked explanation

• Part (a)

  $X\sim\operatorname{Bin}(5,2/5)$. Thus $P(X=2)=\binom52(2/5)^2(3/5)^3=\frac{216}{625}$.

• Part (b)

  Use the complement: $P(X\geq1)=1-P(X=0)=1-(3/5)^5=\frac{2882}{3125}$.

(a) $\frac{216}{625}$.; (b) $\frac{2882}{3125}$.

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