First, we find the total number of marbles.
We add up the red, blue, and yellow marbles:
The number of red marbles is 7 + 4 which equals to 11.
The number of blue marbles is 5.
The number of yellow marbles is 2.
To find the total number, we add these numbers together: 11 (red) + 5 (blue) + 2 (yellow) = 18. So, the total number of marbles is 18.
Second, we find the probability of each event - that is, picking a red marble and then a yellow marble.
Probability is the number of desired outcomes divided by the total number of possible outcomes.
The probability of picking a red marble, denoted as P(red) is the number of red marbles divided by the total number of marbles. So, P(red) = 11 / 18 which is about 0.611 or 61.1%.
The probability of picking a yellow marble, denoted as P(yellow) is the number of yellow marbles divided by the total number of marbles. So, P(yellow) = 2 / 18 which is about 0.111 or 11.1%.
Finally, we can find the answer to our question: What is the probability that Jon selects a red marble and then a yellow marble?
Because these are independent events (selecting a red marble does not affect the chance of selecting a yellow marble next), we can use the multiplication rule of probability to find the overall probability.
The multiplication rule states that the probability of two independent events both happening is the product of their individual probabilities. So the probability of picking a red marble and then a yellow marble, denoted as P(red and yellow), is P(red) * P(yellow).
P(red and yellow) = P(red) * P(yellow) = 0.611 * 0.111 which results in about 0.0679 or 6.8%.
So, the closest option is about 0.043 or 4.3% which seems to be incorrect as our calculated probability is different. There might be a mistake in the question or the provided options.