13. A bag contains 5 red marbles, 3 blue marbles, and 4 yellow marbles. A students removes 1 marble without looking, records the colour, then returns the marble to the bag. The process is repeated. What is the probability of NOT a red marble, then NOT a yellow marble?
12 marbles. 7 not red, 8 not yellow. So,
7/12 * 8/12
To determine the probability of NOT getting a red marble and then NOT getting a yellow marble, we need to calculate the probability of each event separately and then multiply them together.
1. Probability of NOT getting a red marble:
There are a total of 5 red marbles out of 12 marbles in the bag. When a marble is drawn and replaced, the number of marbles remains the same. So for the first event (NOT getting a red marble), the probability can be calculated as:
P(NOT red) = Number of non-red marbles / Total number of marbles
P(NOT red) = (3 blue marbles + 4 yellow marbles) / 12 total marbles
P(NOT red) = 7 / 12
2. Probability of NOT getting a yellow marble:
Similarly, there are a total of 4 yellow marbles out of the 12 marbles in the bag. So for the second event (NOT getting a yellow marble), the probability is:
P(NOT yellow) = Number of non-yellow marbles / Total number of marbles
P(NOT yellow) = (5 red marbles + 3 blue marbles) / 12 total marbles
P(NOT yellow) = 8 / 12
To find the probability of both events happening (NOT red and then NOT yellow), we multiply the probabilities together:
P(NOT red, then NOT yellow) = P(NOT red) * P(NOT yellow)
P(NOT red, then NOT yellow) = (7 / 12) * (8 / 12)
P(NOT red, then NOT yellow) ≈ 0.39 or 39%
Therefore, the probability of not drawing a red marble, then not drawing a yellow marble is approximately 0.39 or 39%.