There is a jar containing 100 marbles: 40 of the marbles are red, 30 are blue, 20 are white, and 10 are black. You are blindfolded and select one marble at random, record the color, and put the marble back in the jar, and shake the jar. You continue this process indefinitely. What is the probability that the first time you draw a black marble is on the 4 th attempt?

Step 1 ：The problem is asking for the probability that the first black marble is drawn on the 4th attempt. This means that the first three draws must not be black, and the fourth draw must be black.

Step 2 ：Since the draws are with replacement, the probability of drawing a black marble remains constant at \(\frac{10}{100} = 0.1\), and the probability of not drawing a black marble is \(1 - 0.1 = 0.9\).

Step 3 ：The probability of this sequence of events is the product of the probabilities of each individual event.

Step 4 ：Let's denote the probability of not drawing a black marble as \(prob\_not\_black = 0.9\) and the probability of drawing a black marble as \(prob\_black = 0.1\).

Step 5 ：Then, the probability that the first time you draw a black marble is on the 4th attempt is \(prob\_4th\_black = prob\_not\_black^3 \times prob\_black = 0.0729\).

Step 6 ：Final Answer: The probability that the first time you draw a black marble is on the 4th attempt is \(\boxed{0.0729}\).