17 An online company is tracking the timing and condition of its deliveries.
The probability that a parcel arrives on time is 0.6. When the parcel arrives on time, the probability that it is damaged is 0.1. When the parcel arrives late, the probability that it is damaged is 0.3.
(a) Use the information to complete the tree diagram. [3]
(b) Given that a parcel arrives damaged, find the probability that it also arrived on time. [4]
Mark scheme (a)
Answer
Marks
Part marks and guidance
Fully correct diagram
3
B1 0.4 and 0.9 correctly placed
B2 0.3 and 0.7 correctly placed or B1 for 0.3 correctly placed or for 0.3 and 0.7 switched
Mark scheme (b)
Answer
Marks
Part marks and guidance
\(\frac{1}{3}\)
4
M3 for \(\frac{0.6 \times 0.1}{0.6 \times 0.1 + \textit{their}(0.4 \times 0.3)}\) oe or M2 for \(0.6 \times 0.1 + \textit{their}(0.4 \times 0.3)\) or better implied by 0.18 or M1 for \(0.6 \times 0.1\) implied by 0.06 or for \(\textit{their}(0.4 \times 0.3)\) implied by 0.12
