The probability of having to vacuum and then mow the lawn is .91.

To find the probability of selecting a red marble (vacuuming) first and then a yellow marble (mowing the lawn), you need to use the formula for probability when drawing without replacement: (number of desired outcomes) / (total number of possible outcomes). For the first draw, there are 5 red marbles out of a total of 28 marbles (5 red + 7 blue + 3 green + 4 black + 9 yellow = 28). So the probability of drawing a red marble first is 5/28. For the second draw, there is now one less marble in the jar, so there are a total of 27 marbles. Since you want to draw a yellow marble next, there are 9 yellow marbles left. So, the probability of drawing a yellow marble after drawing a red marble is 9/27. To find the probability of both events occurring in sequence, you need to multiply the probabilities together: (5/28) * (9/27) You can simplify the fractions by dividing the numerator and denominator with common factors: (5/28) * (1/3) = (5*1)/(28*3) = 5/84 Now, convert this fraction to a decimal by dividing the numerator by the denominator: 5 ÷ 84 ≈ 0.0595 When you round to the nearest thousandth, you get: 0.060 Therefore, the probability of having to vacuum and then mow the lawn when drawing two marbles without replacement is approximately 0.060.