Question

In a certain computer, the probability of a memory failure is 0.01, while the probability of a hard disk failure is 0.02. If the probability that the memory and the hard disk fail simultaneously is 0.0014, then
(a) Are memory failures and hard disk failures independent events?

Answer 1

Answer:

We need to remember that we have independent events when a given event is not affected by previous events, and we can verify if two events are independnet with the following equation:

$P(A \cap B) = P(A) *P(B)$

For this case we have that:

$P(A) *P(B) = 0.01*0.02= 0.0002$

And we see that $0.0002 \neq P(A \cap B)$

So then we can conclude that the two events given are not independent and have a relationship or dependence.

Step-by-step explanation:

For this case we can define the following events:

A= In a certain computer a memory failure

B= In a certain computer a hard disk failure

We have the probability for the two events given on this case:

$P(A) = 0.01 , P(B) = 0.02$

We also know the probability that the memory and the hard drive fail simultaneously given by:

$P(A \cap B) = 0.0014$

And we want to check if the two events are independent.

We need to remember that we have independent events when a given event is not affected by previous events, and we can verify if two events are independnet with the following equation:

$P(A \cap B) = P(A) *P(B)$

For this case we have that:

$P(A) *P(B) = 0.01*0.02= 0.0002$

And we see that $0.0002 \neq P(A \cap B)$

So then we can conclude that the two events given are not independent and have a relationship or dependence.