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 20 marbles consisting of 1​ red, 14 ​blue, and 5 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.       Question content area bottom Part 1 a. Choose the correct answer below.     A. The two events are independent because the​ 5% guideline can be applied in this case.   B. The two events are independent because the occurrence of one does not affect the probability of the occurrence of the other.   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 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. Part b. The probability that events A and B both occur is enter your response here. ​(Round to four decimal places as​ needed.)

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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
20
marbles consisting of 1​ red,
14
​blue, and
5
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.
 
 
 

Question content area bottom

Part 1
a. Choose the correct answer below.
 
 
A.
The two events are independent because the​ 5% guideline can be applied in this case.
 
B.
The two events are independent because the occurrence of one does not affect the probability of the occurrence of the other.
 
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 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.
Part b.
The
probability that events A and B both occur is
enter your response here.
​(Round to four decimal places as​ needed.)
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