*use the following data
Alan places five white marbles and five black marbles into a bag. He then performs the two experiments described below to select two marbles from the bag.
one marble is selected from the bag and replaced before a second marble is selected.
one marble is selected from the bag and NOT replaced before a second marble is selected.
The following two events are the same for each experiment:
EVENT X: the first marble selected is black.
EVENT Y: the second marble
1. In the first experiment, event X and event Y are ` ``i` ,and in the second experiment, event X and event Y are ` ``ii` .
Row `i` `ii`
A. dependent independet
B. dependent dependent
C. independent independent
D. independent dependent
The question is asking about whether the outcomes of event y are dependent on the results of x, and denoting them by lower-case roman numerals.
In experiment 1(i) drawing a black marble first doesn't affect the probability of drawing a black or white marble for event y, because the marble was placed back in the bag so the probability remained 5/10 or 1/2 so Events X and Y are independent.
In Experiment 2(ii) drawing a black marble first does affect the probabilities of event y, because the number of total marbles is now 9 and the number of black marbles is now 4. So event y is not independent of event x, because x changed the probabilities.
A. cannot be right because it has them classified the other way around.
B. Cannot be right because it classifies i as dependent when it is independent
C. Cannot be right because it classifies ii as independent when it is dependent
D. Is correct. i is independent and ii is dependent.