SOLUTION: A certain delivery service offers both express and standard delivery. Eighty percent of parcels are sent by standard delivery, and 20% are sent by express. Of those sent standard,

Question 1019458: A certain delivery service offers both express and standard delivery. Eighty percent of parcels are sent by standard delivery, and 20% are sent by express. Of those sent standard, 75% arrive the next day, and of those sent express, 94% arrive the next day. A record of a parcel delivery is chosen at random from the company's files.

a. What is the probability that the parcel was shipped express and arrived the next day?

Answer by mathmate(429) (Show Source): You can put this solution on YOUR website!

Question:
A certain delivery service offers both express and standard delivery. Eighty percent of parcels are sent by standard delivery, and 20% are sent by express. Of those sent standard, 75% arrive the next day, and of those sent express, 94% arrive the next day. A record of a parcel delivery is chosen at random from the company's files.
a. What is the probability that the parcel was shipped express and arrived the next day?

Summary of given information:
standard delivery=80%
express=20%
Next day delivery for standard=75%
Next day deliver for express = 94%

Solution:
E=Event of shipping express
N=event of arriving next day
We look for the probability of a randomly selected parcel shipped express and arrived the next day. This is obtained by the multiplication of the two ratios, similar to a two-step experiment.
P(E∩N)=P(E)*P(N)=0.20*0.94=0.188
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