# *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. FIRST EXPERIMENT...

*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.

FIRST EXPERIMENT

one marble is selected from the bag and replaced before a second marble is selected.

SECOND EXPERIMENT

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**

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### 1 Answer

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.