How do I solve this question? A school lab has sixteen computers. A teacher observes that, in the long run, in 80% of school days, at least 1 machine is not working properly. Assuming the probability of a computer not working properly is independent of the others, find the probability that: a) a randomly chosen computer is not working in any school day. b) at least 2 computers are not working properly in any school day

2k1ablakrh0

2k1ablakrh0

Answered question

2022-09-25

How do I solve this question?
A school lab has sixteen computers. A teacher observes that, in the long run, in 80% of school days, at least 1 machine is not working properly. Assuming the probability of a computer not working properly is independent of the others, find the probability that:
a) a randomly chosen computer is not working in any school day
b) at least 2 computers are not working properly in any school day
Attempt: I’m really not sure how to approach this question. If for 80% of school days at least 1 computer doesnt work that means for 20% of school says at least 15 doesnt work. Now do you use the binomial expansion to find for all school days?

Answer & Explanation

Cassie Moody

Cassie Moody

Beginner2022-09-26Added 10 answers

Step 1
We know that 0.8 = P ( broken PCs  1 ). So:
0.2 = P ( broken PCs  < 1 ) = P ( broken PCs  = 0 ) = ( 1 p ) 16 ,
where p is the probability for the j-th computer to be broken. This p is the answer for the first question.
Step 2
For the second one: we want to calculate q = P ( broken PCs  2 ). So:
1 q = P ( broken PCs  < 2 ) = P ( broken PCs  = 0 ) + P ( broken PCs  = 1 ) = ( 1 p ) 16 + ( 16 1 ) p ( 1 p ) 15 .
This q is the answer to your second question.

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