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

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 10 marbles consisting of 1 red, 3 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 independent because the occurrence of one does not affect the probability of the occurrence of the other. B. 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. C. 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. D. The two events are independent because the 5% guideline can be applied in this case. b. The probability that events A and B both occur is

Explanation / Answer

total marbles:10

=1 red+3 blue+6 green

green balls=6

5%(10)=1/2=0.5

The two events are technically dependent but are treated as independent because 6>5% of 10. Picking the green marble for all practical purposes does not affect the chances of picking a red marble.

ANSWER B IS CORRECT ANSWER

SOLUTIONB:'

selecting green ball=6/10=3/5=0.6

selecting red marble=1/9

joint probability=6/10*1/9=6/90=2/30=1/15

The probability that events Aand B both occur is 1/15

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