Question 1168310
This problem can be solved using the Poisson distribution, which is used to model the probability of a given number of events occurring in a fixed interval of time or space if these events occur with a known average rate and independently of the time since the last event.

**1. Understand the Poisson Distribution**

* The Poisson distribution formula is: P(X = k) = (e^(-λ) * λ^k) / k!
    * P(X = k) is the probability of k events occurring.
    * λ (lambda) is the average number of events (in this case, babies born with hair on their backs).
    * e is Euler's number (approximately 2.71828).
    * k! is the factorial of k.

**2. Identify the Values**

* λ = 3 (average number of babies born with hair on their backs per day)
* k = 0 (we want to find the probability of no babies born with hair on their backs)

**3. Apply the Poisson Formula**

* P(X = 0) = (e^(-3) * 3^0) / 0!
* P(X = 0) = (e^(-3) * 1) / 1
* P(X = 0) = e^(-3)

**4. Calculate the Probability**

* e^(-3) ≈ 0.049787

**5. Round to 4 Decimal Places**

* P(X = 0) ≈ 0.0498

**Therefore, the probability that no babies are born with hair on their backs in one day is approximately 0.0498.**