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Math  /  Data & Statistics

QuestionMail works as an IT technician for a local company. There are 1000 computers on the company's network and 958 of them are not infected with a wirus Mai chooses a computer on the company's notwork at random. Tef the event AA and the event BB he act followe. A: The computer Mal chooses is not infected with the virus. B: The computer Mai chooses is infected with the virus. Find the following probabilities. Write vour answers as deelmal numbers and do not round. P(A)=P(A)= □\square P(B)=P(B)= □\square

Studdy Solution

STEP 1

1. There are a total of 1000 computers on the company's network.
2. 958 computers are not infected with the virus.
3. Event A A is that a computer chosen is not infected.
4. Event B B is that a computer chosen is infected.

STEP 2

1. Calculate the probability of event A A .
2. Calculate the probability of event B B .

STEP 3

Calculate the probability of event A A , which is the probability that a randomly chosen computer is not infected. This is given by the ratio of the number of not infected computers to the total number of computers.
P(A)=Number of not infected computersTotal number of computers=9581000P(A) = \frac{\text{Number of not infected computers}}{\text{Total number of computers}} = \frac{958}{1000}

STEP 4

Calculate the probability of event B B , which is the probability that a randomly chosen computer is infected. This can be found by subtracting the probability of event A A from 1, or by directly calculating the ratio of the number of infected computers to the total number of computers.
First, find the number of infected computers:
Number of infected computers=1000−958=42\text{Number of infected computers} = 1000 - 958 = 42
Now, calculate P(B) P(B) :
P(B)=Number of infected computersTotal number of computers=421000P(B) = \frac{\text{Number of infected computers}}{\text{Total number of computers}} = \frac{42}{1000}
The probabilities are:
P(A)=0.958P(A) = 0.958
P(B)=0.042P(B) = 0.042

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