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Answer:
(a) The probability that a randomly selected parcel arrived late is 0.026.
(b) The probability that a parcel was late was being shipped through the overnight mail service A₁ is 0.615.
(c) The probability that a parcel was late was being shipped through the overnight mail service A₂ is 0.192.
(d) The probability that a parcel was late was being shipped through the overnight mail service A₃ is 0.192.
Step-by-step explanation:
Consider the tree diagram below.
(a)
The law of total probability sates that:
Use the law of total probability to determine the probability of a parcel being late.
Thus, the probability that a randomly selected parcel arrived late is 0.026.
(b)
The conditional probability of an event A provided that another event B has already occurred is:
Compute the probability that a parcel was late was being shipped through the overnight mail service A₁ as follows:
Thus, the probability that a parcel was late was being shipped through the overnight mail service A₁ is 0.615.
(c)
Compute the probability that a parcel was late was being shipped through the overnight mail service A₂ as follows:
Thus, the probability that a parcel was late was being shipped through the overnight mail service A₂ is 0.192.
(d)
Compute the probability that a parcel was late was being shipped through the overnight mail service A₂ as follows:
Thus, the probability that a parcel was late was being shipped through the overnight mail service A₃ is 0.192.
