for the given pair of events A and B, complete parts (a) and (b) below. Score: 0
ID: 3221784 • Letter: F
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for the given pair of events A and B, complete parts (a) and (b) below. Score: 0 of 1 pt 7 of 15 (6 complete) HW Score: 33.33%, 5 of 15 pts 4.4.11 Question Help For the given pair of events and complete parts (a) and (b) below, A A marble is randomly selected from abag containing 11 martles consisting of 1 red 4 blue, and 6 green marbles. The selected matle isore ofthe green 1 B: Asecond marble is selected and it is the 1 red marble in the bag. a Determine whether events Aand Bare independent or dependent. or two events are technicaly dependent but can be treated as f they are independent according to the 5%guideline, consider them to be independent) Find PIA and B) the probability that events AandB both occur. a. Choose the correct answer below. A The two events are dependent because the occurrence of one affects the probablity of the occurrence of the other and the 5% guideline can be appled in B. The two events are independent because the occurrence of one does not affect the probabilty of the occurrence of the other. Mc 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 appled D. The two events are independent because the 5% guideline can be appled in this case. b. The probability that events A and B both occur is (Round to four decimal places as needed.)Explanation / Answer
P(A) = 6C1 /11C1= 6/11
P(B) = 1/11
(a) The events are technically dependent as P(B) depends on the event A occurring.
Now lets see Thais 5% guideline. It is treating Dependent Events as Independent: 5% Guideline for Cumbersome Calculations When calculations with sampling are very cumbersome and the sample size is not more than 5% of the size of the population, treat the selections as being independent (even if they are actually dependent). Here it is not the case of 5% guideline as population size is pretty small as n <=0.05N.
so the answer is option 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.
(b) Probability of A and B both occurring. P(A and B) = P(A and B) = P(A) P(B|A) = 6/11 * 1/10 = 3/55
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