Given the following probabilities for choosing 2 marbles from a bag of 10 marbles, determine if the events are dependent or independent. p(blue) = 3/10, p(green) = 1/5, p(blue and green) = 3/100

ANSWER

The events are dependent

EXPLANATION

The selection is done without replacement, so the probability of one event occurring affects the other.

For instance, after the first marble is chosen, the sample space reduces and this affects the probability of choosing the second marble.

Also, we were given that,





and



Since


The events are not mutually exclusive, hence they are dependent.

Also note that, events A and B are independent if and only if



Otherwise, A and B are dependent events.

Since



The events are dependent.