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Chapter 6: Problem 85

A certain company sends \(40 \%\) of its overnight mail parcels by means of express mail service \(A_{1}\). Of these parcels, \(2 \%\) arrive after the guaranteed delivery time (use \(L\) to denote the event late delivery). If a record of an overnight mailing is randomly selected from the company's files, what is the probability that the parcel went by means of \(A_{1}\) and was late?

Short Answer

Expert verified
The probability that the parcel went by means of \(A_{1}\) and was late is \(0.008\) or \(0.8\%\).

Step by step solution

01

Identify the Probabilities of Individual Events

From the problem, it's known that the probability of a parcel being sent by means of service A1, denoted as \(P(A1)\), is \(40\%\), or \(0.4\) in decimal terms. The probability of a parcel arriving late given that it was sent by A1, denoted as \(P(L | A1)\), is \(2\%\), or \(0.02\) in decimal terms.
02

Compute the Intersection of the Two Events

The probability of intersection of two events (i.e., the parcel being sent by A1 and arriving late) can be calculated as: \(P(A1 \cap L) = P(A1) \times P(L | A1)\).
03

Calculate the Result

Substituting the values into the formula, we get: \(P(A1 \cap L) = 0.4 \times 0.02 = 0.008\).

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Most popular questions from this chapter

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