There is a 0.125 probability that you will have to vacuum and then mow the lawn.

To find the probability of drawing a red marble (vacuuming) first and then a yellow marble (mowing the lawn) without replacement, we must first determine the total number of marbles in the jar. 5 red + 7 blue + 3 green + 4 black + 9 yellow = 28 marbles The probability of drawing a red marble first (vacuuming) is the number of red marbles divided by the total number of marbles: P(red) = 5 red marbles / 28 total marbles = 5/28 After the red marble has been drawn, there are now 27 total marbles in the jar. The probability of drawing a yellow marble(mowing the lawn) second is the number of yellow marbles divided by the new total number of marbles in the jar: P(yellow) = 9 yellow marbles / 27 total marbles = 9/27 Now, to find the probability of both events happening in sequence, we multiply their probabilities: P(red then yellow) = P(red) × P(yellow) = (5/28) × (9/27) P(red then yellow) = 45/756 Now, let's express the answer as a decimal rounded to the nearest thousandth: P(red then yellow) ≈ 0.060 So the probability of drawing a red marble (vacuuming) and then a yellow marble (mowing the lawn) without replacement is approximately 0.060 or 6%.