Question

An example of dependent events is drawing a red marble out of one jar and then drawing a

red marble out of the same jar, after replacing the first marble.

green marble out of the same jar, without replacing the first marble.

green marble out of another jar.

red marble out of another jar.

Answer 1

Second Option:

"green marble out of the same jar, without replacing the first marble"

Explanation:

Two events r and s are independent if the probability that r occurs does not affect the probability that s occurs.

When choosing an object of some color b from a jar with n objects where there are x objects of the desired color b, the probability of obtaining 1 object of color b when randomly selecting an object from the jar is:

`P_1 =(x)/(n)`

If after taking the object it does not return it to the jar (without replacement) then, now the probability of obtaining an object of color b is:

`P_2 = (x-1)/(n-1)` if the one selected in the first trial was the color b.

`P_2 = (x)/(n-1)` if the one selected in the first test was not the color b

Note that now the probability P depends on the result obtained in the previous test.

This event is dependent.

However, if by take object b in the first test, and the object is returned to the jar, and then the second test is made, then

`P_1 = P_2`.

The probability does not depend on the result of the first trial. The same happens if the objects are taken from different jars.

These would be independent events.

Finally the correct option is the second option.