A batch of 425 containers for frozen orange juice contains 4 that are defective. Two are selected, at random, without replacement from the batch. a) What is the probability that the second one selected is defective given that the first one was defective? Round your answer to five decimal places (e.g. 0.98765). i b) What is the probability that both are defective? Round your answer to seven decimal places (e.g. 0.9876543). c) What is the probability that both are acceptable? Round your answer to three decimal places (e.g. 0.987). Three containers are selected at random without replacement from the hatch

A First Course in Probability (10th Edition)
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Chapter1: Combinatorial Analysis
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A batch of 425 containers for frozen orange juice contains 4 that are defective. Two are selected, at random, without
replacement from the batch.
a) What is the probability that the second one selected is defective given that the first one was defective? Round your
answer to five decimal places (e.g. 0.98765).
i
b) What is the probability that both are defective? Round your answer to seven decimal places (e.g. 0.9876543).
i
c) What is the probability that both are acceptable? Round your answer to three decimal places (e.g. 0.987).
i
Three containers are selected, at random, without replacement, from the batch.
d) What is the probability that the third one selected is defective given that the first and second one selected were
defective? Round your answer to three decimal places (e.g. 0.987).
i
e) What is the probability that the third one selected is defective given that the first one selected was defective and the
second one selected was okay? Round your answer to five decimal places (e.g. 0.98765).
i
f) What is the probability that all three are defective? Round your answer to three decimal places (e.g. 0.987).
Transcribed Image Text:A batch of 425 containers for frozen orange juice contains 4 that are defective. Two are selected, at random, without replacement from the batch. a) What is the probability that the second one selected is defective given that the first one was defective? Round your answer to five decimal places (e.g. 0.98765). i b) What is the probability that both are defective? Round your answer to seven decimal places (e.g. 0.9876543). i c) What is the probability that both are acceptable? Round your answer to three decimal places (e.g. 0.987). i Three containers are selected, at random, without replacement, from the batch. d) What is the probability that the third one selected is defective given that the first and second one selected were defective? Round your answer to three decimal places (e.g. 0.987). i e) What is the probability that the third one selected is defective given that the first one selected was defective and the second one selected was okay? Round your answer to five decimal places (e.g. 0.98765). i f) What is the probability that all three are defective? Round your answer to three decimal places (e.g. 0.987).
Expert Solution
Step 1: Given Information:

“Since you have asked multiple sub part questions, we will solve the first three questions for you. If you want any specific questions to be solved then please specify the question number or post only that question.”

Given that,

the total number of containers = 425

number of defective containers = 4

Non defective containers = 425- 4 = 421

The formula to calculate the Probability

P(A) = fraction numerator N u m b e r space o f space f a v o u r a b l e space c a s e s over denominator T o t a l space n u m b e r space o f space c a s e s end fraction

P(B|A) = fraction numerator P left parenthesis A intersection B right parenthesis over denominator P left parenthesis A right parenthesis end fraction

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