Mathematics 9709 · AS & A Level · Probability

Probability — practice question

On each day Alexa goes to work, the probabilities that she travels by bus, by train or by car are $0.4$, $0.35$ and $0.25$ respectively. If she goes by bus, the chance that she is late is $0.55$. If she goes by train, the chance that she is late is $0.7$. If she goes by car, the chance that she is late is $x$. For a day chosen at random when Alexa goes to work, the probability that she is not late is $0.48$.
(a)[3]

Find the value for $x$.

(b)[3]

Find the probability that Alexa goes to work by train, given that she arrives late.

Worked solution & mark scheme

This 6-mark question has a full step-by-step worked solution and mark scheme. One marking point: Correct weighted-probability equation, for instance $0.4p+0.35q+0.25r$.

  • Full mark scheme, point by point
  • Step-by-step worked solution
  • Write your answer & get it marked instantly by AI