Question

The article "Birth Beats Long Odds for Leap Year Mom, Baby" (San Luis Obispo Tribune, March 2, 1996) reported that a leap year baby (someone born on February 29 ) became a leap year mom when she gave birth to a baby on February \(29,1996 .\) The article stated that a hospital spokesperson said that the probability of a leap year baby giving birth on her birthday was one in \(2.1\) million (approximately .00000047). a. In computing the given probability, the hospital spokesperson used the fact that a leap day occurs only once in 1461 days. Write a few sentences explaining how the hospital spokesperson computed the stated probability. b. To compute the stated probability, the hospital spokesperson had to assume that the birth was equally likely to occur on any of the 1461 days in a four- year period. Do you think that this is a reasonable assumption? Explain. c. Based on your answer to Part (b), do you think that the probability given by the hospital spokesperson is too small, about right, or too large? Explain.

Short answer

The spokesperson calculated the probability by multiplying the chances of each independent event (being born and giving birth on a leap day). The assumption of equal birth likelihood across the 1461 days may not be entirely accurate due to factors influencing birth rates, but it's reasonably used for simplicity. Consequently, the provided probability of being both a leap year baby and mom could be roughly correct under these assumptions.

Step-by-step solution

Understanding the Probability Calculation

As stated in the exercise, a leap day occurs once in 1461 days (which are the total days in 4 years). Therefore, the chance of a person being born on a leap day, and then giving birth on a leap day would be \(1/1461 * 1/1461 = 1/2.134*10^6 = 0.0000004683\). This is approximately equal to \(0.00000047\), as stated by the hospital spokesperson. Hence, the spokesperson is merely multiplying the probabilities of the two independent events.

Evaluating the Assumption

The assumption made by the hospital spokesperson is that a birth is equally likely to occur on any of the 1461 days in a four-year period. Realistically, this might not be completely accurate since birth rates can vary due to factors such as season, weather, and cultural practices among others. However, without specific birth data to suggest otherwise and for simplicity, it can be seen as a reasonable assumption.

Evaluating the Provided Probability

The calculated probability already assumes that births are equally distributed throughout the year. Given our discussion in Step 2, if we consider variations in birth rates due to factors like seasonality, the probability could be slightly higher or lower. However, without specific data, we cannot make a definitive statement and thus the provided probability seems roughly correct given the used assumption.