Answer:
55.32% probability that a late package was delivered by express delivery service 2
Step-by-step explanation:
Bayes Theorem:
Two events, A and B.
In which P(B|A) is the probability of B happening when A has happened and P(A|B) is the probability of A happening when B has happened.
In this question:
Event A: Late delivery.
Event B: Service 2 was used.
A certain company sends 35% of its overnight mail parcels via express delivery service 1 and the rest by express delivery service 2.
100 - 35 = 65%.
So
Service 2 has a record of 2.0% of packages being delivered late.
This means that
Probability of a late delivery.
35% from service 1. Of those, 3% are late.
65% from service 2. Of those, 2% are late.
So
What is the probability that a late package was delivered by express delivery service 2
55.32% probability that a late package was delivered by express delivery service 2