For the given pair of events A and B complete parts a and b

For the given pair of events A and B. complete parts (a) and (b) below. A marble is randomly selected from a bag containing 13 marbles consisting of 1 red. 9 blue. and 3 green marbles. The selected marble is one of the green marbles. A second marble is selected and it is the 1 red marble in the bag. Determine whether events A and B are independent or dependent. (If two events are technically dependent but can be treated as if they are independent according to the 5% guideline. Consider them to be independent.) Find P(A and B), the probability that events A and B both occur.

Solution

a)

The 2 events are independent because the ocurrence of one does not affect the probability of the ocurrence of the other

b)

1 green marble

3C1 / 13C1 = 0.2308

1 red marble

1C1 / 12C1 = 0.083

P( A and B) = 0.083 * 0.2308 = 0.0192