You have recently purchased a product through e-commerce. The delivery that carries the product has 4 possible routes with identical delivery tỉme between A and B. If he chooses a random route between: 1-3-4, 1-2, 1-6-4 or 1-5, and in each of the 6 sections that make up these routes, there is a 0.31 probability of being delayed, what is the probability that it meets the delivery time? Assume that the delays in each leg occur independently. The following Figure illustrates the three possible routes: 1 2 B 3.

A First Course in Probability (10th Edition)
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Author:Sheldon Ross
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Chapter1: Combinatorial Analysis
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You have recently purchased a product through e-commerce. The delivery that
carries the product has 4 possible routes with identical delivery time between A
and B. If he chooses a random route between: 1-3-4, 1-2, 1-6-4
or 1-5, and in each of the 6 sections that make up these routes, there is
a 0.31 probability of being delayed, what is the probability that it meets
the delivery time? Assume that the delays in each leg occur
independently.
The following Figure illustrates the three possible routes:
6.
3
1
2
A-
B
Transcribed Image Text:You have recently purchased a product through e-commerce. The delivery that carries the product has 4 possible routes with identical delivery time between A and B. If he chooses a random route between: 1-3-4, 1-2, 1-6-4 or 1-5, and in each of the 6 sections that make up these routes, there is a 0.31 probability of being delayed, what is the probability that it meets the delivery time? Assume that the delays in each leg occur independently. The following Figure illustrates the three possible routes: 6. 3 1 2 A- B
Expert Solution
Step 1

If p is the probability of delay then 1-p is the probability of meeting the delivery time.

Let X1, X2, X3, and X4  are the events of choosing the routes 1-6-4, 1-3-4, 1-2, and 1-5, respectively. Let E is the event of delay in delivery.

Then, PE=PX1PE|X1+PX2PE|X2+PX3PE|X3+PX4PE|X4.

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