"What are the odds?" If Someone Has Been Married and Divorced 3 Times, that a 4th Marriage Lasts?

I received this question from an anonymous source: if someone has been married and divorced 3 times already, what are the chances that a 4th marriage for that person is successful?

The first parameter to define here is what constitutes "success" in a marriage, which presumably is not getting divorced at some point. And this may be morbid, but that means "success" is defined as when one partner dies.

Reliable statistics on the divorce rate are hard to come by since there isn't agreement on using the crude divorce rate (the number of divorces for every 1,000 people in the population) or the refined divorce rate (the number of divorces for every 1,000 married women). For my purposes I'll use the refined divorce rate, since I'm interested in whether someone is already married will get divorced.

The only divorce rates I found broken down by first/second/third marriage have no citation, but it appears to be around 41% of first marriages, 60% of second marriages, and 73% of third marriages end in divorce. There are a variety of suggested reasons for this, but multiple marriages certainly is correlated with a higher divorce rate. Even still, 3.1% of males and 3.2% of females have been married 3+ times, so this scenario is already an unlikely one.

Using these numbers and a logarithmic model, the probability of a 4th marriage ending in divorce should be around 83.61% (16.39% chance of success):

But that's not the best proxy, since as you go through more marriages, you also get older. The U.S. Census has a lot of data on the median duration of each marriage and the duration between each. Of course, the CDC also calculates the life expectancy of different demographic groups. Combining these two sources can give us a good estimate to guess "the odds that a 4th marriage is successful".

Data on first marriages shows that the median age to get married for the first time is 28.3 for males and 25.8 for females. The census data indicates that the median duration of a marriage is 8 years, and upon divorce, the time until getting remarried is about 3.75 years. Which results in the following timelines:

Age At	Male	Female
First	28.3	25.8
Second	36.3	33.8
Third	48.1	45.6
Fourth	59.8	57.3

According to the CDC, the current life expectancy is 71.8 for males and 78.8 for females. This leaves a much shorter timeline (12 years) for men from the expected time of the 4th marriage to their life expectancy, compared to women (21.5 years).

I then used the available sample data to figure out the standard deviation in marriage lengths, which is around 14.08 years. Using an exponential distribution (which is memoryless, so the elapsed length of the marriage does not influence the likelihood of another divorce) gives the estimated probabilities that a male and female do not get divorced from the 4th marriage over a period of 12 and 21.5 years, respectively: 22.31% for the male and 6.81% for the female.