A file contains 1Kbytes (i.e. 1000 bytes). The probability that there

sputavanomr

sputavanomr

Answered question

2021-11-17

A file contains 1Kbytes (i.e. 1000 bytes). The probability that there exists at least one corrupted byte is 0.01. The probability that at least two bytes are corrupted is 0.005. Let the outcome of the experiment be the number of bytes in error.
a) Define the sample space.
b) Find the probability of no errors.
c) Find the probability of exactly one byte in error.
d) Find the probability of at the most one byte is in error.

Answer & Explanation

memomzungup4

memomzungup4

Beginner2021-11-18Added 14 answers

Step 1
Given information:
Given that the file consists of 1000 bytes.
The probability that there exists at least one corrupted byte is 0.01.
The probability that at least two bytes are corrupted is 0.005.
Step 2
a) Define the sample space:
The set of all possible outcomes of a probability experiment is called sample space of the experiment.
The sample space for the given experiment is as given below:
S={0, 1, 2, 3, 4, 5, , 997, 998, 999, 1000}
Step 3
b) Find the probability of no errors:
The probability of no errors is obtained as given below:
P(X=0)=1P(X1)
=10.01
=0.99
Thus, the probability of no errors is 0.99.
Step 4
c) Find the probability of exactly one byte in error:
The probability of exactly one byte in error is obtained as given below:
P(X=1)=P(X1)P(X2)
=0.010.005
=0.005
Thus, the probability of exactly one byte in error is 0.005.

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