Question

For the given pair of events A and​ B, complete parts​ (a) and​ (b) below. ​

A: A marble is randomly selected from a bag containing 14 marbles consisting of 1​ red, 7 ​blue, and 6 green marbles. The selected marble is one of the green marbles.

​B: A second marble is selected and it is the 1 red marble in the bag.

a. Determine whether events A and B are independent or dependent.​ (If two events are technically dependent but can be treated as if they are independent according to the​ 5% guideline, consider them to be​ independent.)

b. Find​ P(A and​ B), the probability that events A and B both occur.

a. Choose the correct answer below.

A. The two events are dependent because the occurrence of one affects the probability of the occurrence of the other and the​ 5% guideline can be applied in this case.

B. The two events are independent because the​ 5% guideline can be applied in this case.

C. The two events are dependent because the occurrence of one affects the probability of the occurrence of the other and the​ 5% guideline cannot be applied in this case.

D. The two events are independent because the occurrence of one does not affect the probability of the occurrence of the other.

b. The probability that events A and B both occur is ___. ​(Round to four decimal places as​ needed.)

Answer 1

The 5 percent guidelibe suggests that if the sample is no more than 5% of the side of the population then we can consider two technically dependent events to be independent.

Here the population size is 14 and we are taking out 1 marble which is 7.14% of the population size. Hence, the 5% guideline can not be applied in this case.

The occurrence of one event affects the probability of the other hence the events are not independent.

a. Option C is correct.

b. The probability that both events occur is

= The probability that the first marble is green and the second marble is the red one

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