A shipment of 20 computers contains 4 defective machines.Two computers are selected at random without replacement and tested for being detective.
(a). is this a binomial experiment? why or why not
solution.
Yes. because each trial can result in just two possible outcomes.
(b). What is the probability that both computers are detective.
solution.
16/20sound(s)
4/20detectives(D)
p(D1)and P(D2)
(C).What is the probability that atleast one is detective?
solution
P('SS)
=1-P(SS)
To find the probability that both computers are defective, you first need to calculate the probability of selecting a defective computer on the first trial and then multiply it by the probability of selecting a defective computer on the second trial.
Given that there are initially 20 computers, out of which 4 are defective, the probability of selecting a defective computer on the first trial is:
P(D1) = Number of defective computers / Total number of computers = 4 / 20 = 1/5
Since the first computer is not replaced, the probability of selecting a defective computer on the second trial is:
P(D2) = Number of remaining defective computers / Remaining total number of computers = 3 / 19
To find the probability that both computers are defective, you multiply these probabilities together:
P(both defective) = P(D1) * P(D2) = (1/5) * (3/19) = 3/95
Therefore, the probability that both computers selected are defective is 3/95.
For the second part, to find the probability that at least one computer is defective, you need to find the complement of the probability that both computers are non-defective.
The probability that both computers are non-defective is:
P(SS) = Number of non-defective computers / Total number of computers = (20 - 4) / 20 = 16/20 = 4/5
Now, to find the probability that at least one computer is defective, you subtract the probability of both computers being non-defective from 1:
P(at least one defective) = 1 - P(SS) = 1 - 4/5 = 1/5
Therefore, the probability that at least one computer is defective is 1/5.