Conditional binomial probability

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

3 practice marks

Original practice question

A fair coin is tossed 4 times independently. X is the number of heads. (a) Find $P(X\geq1)$. [1 marks] (b) Given at least one head, find the probability of exactly two heads. [2 marks]

Worked explanation

• Part (a)

  The complement is four tails, of probability $(1/2)^4=1/16$, giving $15/16$.

• Part (b)

  $P(X=2)=\binom42/16=6/16$. Divide by $15/16$ to get $P(X=2\mid X\geq1)=6/15=2/5$.

(a) $15/16$.; (b) $2/5$.

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