I’m currently in statistics and I just wanted to make a calculation for fun and

Question

I’m currently in statistics and I just wanted to make a calculation for fun and see if I’m right. My job employs 83 people and every month 10% of them are randomly selected to take a drug test. Of the 10% select, only 30% of the samples are actually tested. What is the probability that someone will be selected to take a drug test and their sample will be tested? I did,
(83)*0.10=8.3 then rounded up to 9. So 9 are selected to test.
So 9 people are selected to (9)*(0.3)= 2.7 then rounded up to 3. So 3 are actually tested. The ended result is (1/83)*(3/9)=0.4%
Is this correct? I’m currently in statistics and I just wanted to make a calculation for fun and see if I’m right. My job employs 83 people and every month 10% of them are randomly selected to take a drug test. Of the 10% select, only 30% of the samples are actually tested. What is the probability that someone will be selected to take a drug test and their sample will be tested? I did,
(83)*0.10=8.3 then rounded up to 9. So 9 are selected to test.
So 9 people are selected to (9)*(0.3)= 2.7 then rounded up to 3. So 3 are actually tested. The ended result is (1/83)*(3/9)=0.4%
Is this correct? My job employs 83 people and every month 10% of them are randomly selected to take a drug test. Of the 10% select, only 30% of the samples are actually tested. What is the probability that someone will be selected to take a drug test and their sample will be tested? I did,
(83)*0.10=8.3 then rounded up to 9. So 9 are selected to test.
So 9 people are selected to (9)*(0.3)= 2.7 then rounded up to 3. So 3 are actually tested. The ended result is (1/83)*(3/9)=0.4%
Is this correct?

Explanation / Answer

Not quite correct although conceptually perfect.

Why round off and get an answer in error.

Instead, 30% of 10% is 3%. So, probability = 0.03 ANSWER

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