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A warehouse has 5,000 drums of liquid chemicals. The foreman knows that 50 of these drums contain off-quality chemicals. Assume that the drum is replaced each time before sampling. What is the probability that none of 3 drums he selects at random are off-quality?



(1/100)_

(50x49x48)/(5,000_)

(99/100)_

Verified Answer :

Edufirst

Given that the drum is replaced each time before sampling, the selections are independent events. Then, the probability of the combined event is the product of each probability: (50/5000) (50/5000) (50/5000) = (1/100)^3 = 0.000001

Answer:

(\frac{99}{100} )^3

Explanation:

Given that A warehouse has 5,000 drums of liquid chemicals. The foreman knows that 50 of these drums contain off-quality chemicals.

Now first one drum is drawn

Prob that this drum is not off quality =4950/5000 =0.99

Next one drum is replaced.  This replaced may be mixed with others thus making probability for drawing off quality equal to 0.01 every time.

i.e. each trial is independent of the other

Hence prob that none of the drums  he selects at random are off-quality

=0.99x0.99x0.99

=\((\frac{99}{100} )^3\)

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