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 20 marbles consisting of 1 red, 15 blue, and 4 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 he occurrence of he other and e 5 guideline cannot be applied n O B 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 this case. case. ° C. The two events are independent because the occurrence of one does not affect the probability of the occurrence of the other O D. The two events are independent because the 5% guideline can be applied in this case.

Explanation / Answer

part b) P(A) =number of green marbles/ total marbles

= 4/20

=0.2

now after grabbing green marble,we are left with

19 marbles consisting 1 red, 15 blue and 3 green marbles

So P(B) =number red marbles /total marbles left

=1/19

=0.0526

P(A n B) = P(A)*P(B) =0.2 *0.0526 =0.0105 ( or 1/95)

part a) the two events are dependent because the occurence of one affects the occurence of other and 5% guideline can be applied

so its choice B

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