13. A bag contains 8 red marbles, 4 purple marbles, 5 green marbles, 2 orange, and 1 blue marbles. One marble is selected and replaced. A second marble is selected. Find the
probability of each compound event. Show work and simplify your solutions.
a)
Not selecting an orange marble and then a blue marble
b)
Selecting a green or red marble and then a purple marble

a) 9 / 200

b) 13 / 100

Step-by-step explanation:

a) The two events are independent because they do not depend each other since the marbles are replaced. To find the total probability of two independent events, you multiply the probability of each event together.

Probability is represented by the amount of desirable outcomes over the total number of outcomes. The total would be the number of marbles, which is: 8 + 4 + 5 + 2 + 1 = 20 outcomes. The number of orange marbles is 2, so the outcomes where you do not pick orange are 20 - 2 or 18 outcomes. The probability of not picking an orange marble would be 18 / 20 or 9 / 10 (using the formula for probability).

There is one outcome where we can pick a blue marble, so the probability of picking a blue marble is 1 / 20. Now, we need to multiply the probabilities for each event: 1 / 20 * 9 / 10  = 9 / 200

b)There are 5 green marbles and 8 red marbles, so the the total outcomes where you pick green or red is 13. We put that over our total to get 13 / 20.

There are 4 purple marbles, so the probability of picking purple is 4 / 20 or 1 / 5. Now we multiply the two probabilities to get the total probability: 1 / 5 * 13 / 20 = 13 / 100