Understanding the Probability of Packet Loss in a Congested Network

In summary, the probability that an e-mail with 100 packets will need to be resent is calculated by subtracting the probability that all packets are not lost from 1. This is because the events of packet loss are independent and we can use the complement rule to calculate the probability of one or more packets being lost. Simply multiplying the probability of one packet being lost by 100 is not a valid approach because it does not take into account the possibility of multiple packets being lost. It is important to understand the conditions under which "ANDing" or "ORing" of events corresponds to multiplication or addition of their probabilities in order to properly solve similar problems.
  • #1
francisg3
32
0
a congested computer network has a 0.002 probability of losing a data packet and packet losses are independent events. a lost packet must be resent.

a) what is the probability that an e-mail with 100 packets will need any resent?




i know the answer is P= 1-(1-0.002)^100

however i need some help understanding why it is so. i kno the (1-0.002) si the probability that a packet is not lost. i also know that since there are 100 packets in the e-mail, that there are x^100 chances of it not being lost.

i do not understand why (1-0.002)^100 is subtracted from 1, wouldn't this give the probability that ALL are lost?

also, why can't you just do (probability packets lost)^100?, (0.002)^100
 
Last edited:
Physics news on Phys.org
  • #2
francisg3 said:
a congested computer network has a 0.002 probability of losing a data packet and packet losses are independent events. a lost packet must be resent.

a) what is the probability that an e-mail with 100 packets will need any resent?

i know the answer is P= 1-(1-0.002)^100

however i need some help understanding why it is so. i kno the (1-0.002) si the probability that a packet is not lost. i also know that since there are 100 packets in the e-mail, that there are x^100 chances of it not being lost.

i do not understand why (1-0.002)^100 is subtracted from 1, wouldn't this give the probability that ALL are lost?

(1-0.002) is the probability that a packet is NOT lost.

(1-0.002)^100 is the probability that "the first packet is not lost" AND "the second packet is not lost" AND ... AND "the last packet is not lost".

So (1-0.002)^100 is the probability that NO packets are lost. The complement of that is therefore the probability that one or more packets IS lost.

Notice that it's only when events are independent that we are allowed to multiply probabilities like that.

also, why can't you just do (probability packets lost)^100?, (0.002)^100
Ok you haven't thought that one out very well. But perhaps you really meant to ask "why can't we just use (0.002) * 100". That is, why do we have to deal with the complementary probabilities (and then complement the final result) instead of just dealing with it in a simpler manner. Typically the (erroneous) argument goes like this.

Probability of first packet loss = 0.002
Probability of "first packet loss" OR "second packet loss" = 0.002 + 0.002
Probability of "first packet loss" OR "of second packet loss" OR "of third packet loss" = 0.002 + 0.002 + 0.002

...

Probability of 1st OR of second OR of third OR ... OR of last packet loss = 100 * 0.002

You can easily check that the above gives the wrong answer but it's important to understand why. I want you to think about when (under what conditions) that "ANDing" of events corresponds to simple multiplication of their probabilities. Similarly I want you to think about when "ORing" of events corresponds to simple addition of their probabilities. Truly those things are the key to properly understanding this and similar problems.
 
  • #3
Thanks for the quick reply!
 

What is the difference between statistics and probability?

Statistics is the branch of mathematics that deals with collecting, analyzing, and interpreting data. It involves techniques for organizing and summarizing data, as well as making inferences and predictions based on the data. Probability, on the other hand, is the study of chance and uncertainty. It is the branch of mathematics that deals with calculating the likelihood of events based on known information.

What are the basic principles of probability?

The basic principles of probability include the law of total probability, which states that the sum of the probabilities of all possible outcomes in an experiment must equal 1; the multiplication rule, which states that the probability of two independent events occurring together is the product of their individual probabilities; and the addition rule, which states that the probability of either of two mutually exclusive events occurring is the sum of their individual probabilities.

What is the difference between descriptive and inferential statistics?

Descriptive statistics involves summarizing and describing data, while inferential statistics involves making predictions and drawing conclusions about a larger population based on a smaller sample of data. Descriptive statistics are used to understand and communicate information about a specific group or dataset, while inferential statistics are used to make generalizations and inferences about a larger population.

How is probability used in real life?

Probability is used in many real-life situations, such as predicting the weather, making financial decisions, and assessing risk in medical treatments. It is also used in the fields of business, sports, and gambling to make informed decisions and assess potential outcomes.

What are some common misconceptions about statistics?

One common misconception about statistics is that correlation implies causation. Just because two variables are correlated does not necessarily mean that one causes the other. Another misconception is that a sample size must be large in order to be representative of a population. In reality, a smaller sample size can still accurately represent a larger population if it is chosen randomly and is diverse enough.

Similar threads

  • Engineering and Comp Sci Homework Help
Replies
1
Views
1K
Replies
2
Views
835
Replies
17
Views
1K
  • Engineering and Comp Sci Homework Help
Replies
1
Views
588
  • Other Physics Topics
Replies
31
Views
836
  • Engineering and Comp Sci Homework Help
Replies
13
Views
3K
  • Engineering and Comp Sci Homework Help
Replies
2
Views
1K
  • Engineering and Comp Sci Homework Help
Replies
3
Views
3K
  • Engineering and Comp Sci Homework Help
Replies
6
Views
1K
  • Advanced Physics Homework Help
Replies
1
Views
1K
Back
Top