1)A batch contains 40 bacteria cells. Assume that 12 of the cells are not capabl

Question

1)A batch contains 40 bacteria cells. Assume that 12 of the cells are not capable of cellular replication. Six cells are selected at random, without replacement, to be checked for replication. Round your answers to four decimal places (e.g. 98.7654).

(a) What is the probability that all six cells of the selected cells are able to replicate?

(b) What is the probability that at least one of the selected cells is not capable of replication?

2)

A batch of 484 containers for frozen orange juice contains 6 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. 98.76543).

b) What is the probability that both are defective? Round your answer to seven decimal places (e.g. 98.7654321).

c) What is the probability that both are acceptable? Round your answer to three decimal places (e.g. 98.765).

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. 98.765).

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. 98.76543).

f) What is the probability that all three are defective? Round your answer to three decimal places (e.g. 98.765).

Explanation / Answer

p=12/40=0.3

n=6

a) P(x=0)=BINOM.DIST(0,6,0.3,FALSE)=0.117649

b) P(x>=1)=1-P(0)= 1-BINOM.DIST(0,6,0.3,FALSE)=0.882351

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