A computer virus is trying to corrupt two files. The first file will be corrupted with probability 0.4. Independently of it, the

Question

8 days ago

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second file will be corrupted with probability 0.3. (a) Compute the probability mass function (pmf) of X, the number of corrupted files.

1 answer:

zzz [12.3K] · Answer 1 · 2026-04-08T02:14:32+03:00

Response:

$P(X = 0) = 0.42$

$P(X = 1) = 0.46$

$P(X = 2) = 0.12$

Detailed explanation:

We are presented with the following probabilities:

There is a 40% chance that the first file is corrupted. Thus, there is a 60% chance that the first file is intact.

The second file has a 30% chance of being corrupted, making the chance that it remains intact 70%.

Probability mass function

Probability of each possible outcome (0, 1, or 2 corrupted files).

No files corrupted:

There is a 60% chance that the first file is fine.

Additionally, a 70% chance that the second file is also intact.

So

$P(X = 0) = 0.6*0.7 = 0.42$

Exactly one file corrupted:

In this case, the first one is damaged, while the second remains functional.

This comprises a 40% chance for the first file being corrupted and a 70% chance for the second file being intact.

Alternatively,[the first remains fine with a 60% probability while the second gets corrupted (30%).

Two files corrupted:

A 40% probability applies to the first file being corrupted.

While the second file has a 30% chance of being compromised.

$P(X = 2) = 0.4*0.3 = 0.12$