Simple probability question

If two people (say husband and wife) are in a state with 14.7% unemployment, what is the probability of both of them being unemployed at the same time?

Actual % would be helpful but a formula may be useful in future calculations.

The results are useful for determining free humanitarian help so your answer will go to a good cause. Thanks!

edited: for typo

Assuming that the probability of each being unemployed is independent of the other’s status, it’s the product of the probabilities, i.e., 2.16%. However, in reality the probability is unlikely to be independent. There could be either a positive or a negative correlation, but my guess would be a positive correlation, which would mean that the probability is greater than 2.16%.

It depends on what you mean by your question.

If you mean “If you pick two random people from the labor force, what is the chance that you will choose two unemployed people?”, then it’s 2.16%. If condition A has a 14.7% chance of being true and condition B has a 14.7% chance of being true, the chance of both A AND B being true are (14.7%)*(14.7%) ~= 2.16%

If you mean, “If you pick two random people from the labor force, what is the chance that they both will be unemployed at the same time at some point in the near future?”, then the question is not answerable. The unemployment rate tells you nothing about the likelihood of getting hired or fired.

ETA: Not answerable given only the unemployment rate. Statistics are also maintained for the hiring and firing rate.

Assuming they are independent variables, that is, one being unemployed has no effect on the other being unemployed, the probability that both are unemployed at the same time is 2.2%. You multiply the probabilities getting 0.147 * 0.147 = 0.021609, rounding to 2.2%.

There is a 0.853 * 0.853 = 72.8% probablility that they are both employed, and a 0.147 * 0.853 * 2 = 25.1% probablity that only one is unemployed. The times 2 factor in the last one is because either spouse could be unemployed.

But the question was not about two random people: it was about husband and wife, who are more likely to have various economic and social variables in common than two random people. The probability of their being employed is likely to be correlated, because of the likelihood that one (usually the wife) is staying at home looking after the children. The probability of their being unemployed is more difficult to analyse, because a person can be neither “employed” nor “unemployed”: he or she may be out of the workforce, because not employed and not actively seeking employment.

It’s also possible that the unemployment rate is significantly different for men than for women, or for married people as opposed to single people.

If you want to know what percentage of all married couples in the state have both the husband and the wife unemployed, the 2.2% figure may be the best you can do for a rough estimate, but a better answer would have to be based on data about married couples.

Wow, thanks folks for the quick reply. And you guys are fast!

That 2% probability really says a lot. I just got a request to help a couple (mother in mid 40’s and son in mid 20’s) that moved out of state and claimed joblessness as the reason for moving out of state and requesting help.

There were many other factors that reeked of scam but that math really tells a story by itself. Thanks! (And not just me since the people that really do need help would have been victimized by the scammers.)

If it reeks of scam otherwise, then definitely treat it as one, but a 2.16% probability isn’t really all that low. It’s about 1/46, which is hardly in the range of nearly impossible.

I’d agree, and I’d add that the probability will be higher than 2.16%, because the employment statuses of a parent and an adult child living together are likely to be correlated. The probability could easily be as high as 5%.

Others have described the probabilites; I feel the need to muddy the water. When a place says it has X% unemployment, that does not mean that (100-X)% of the people have jobs. It means, well, a lot of things depending upon how unemployed is defined. But the basic idea is that, of the people who want jobs, X% can’t find them. In a given population most of the people do not even figure into the unemployment stat. Children, the elderly, stay at home wives (yes, and husbands too), bums and illegal aliens don’t appear in the calculation in general.

So, in the OP, if either or both of the people in question does not want a job then there is a large chance that they will not have one and yet they won’t be part of the unemployment count.

This is one of those interesting username/post juxtapositions. :slight_smile:


Absolutely correct. In fact, after several months into a recession, when you hear unemployment figures quoted in the media, it will often be accompanied by a caveat like, “Unemployment figures were down slightly this month, but only because a large proportion of the unemployed gave up on finding work after so many months and so are no longer counted as unemployed.”

Thanks for the help, everyone!

I agree that the underemployment figures may be understated (but also maybe overstated given the number of people that work “off” the books).

The 2.16% does, however, really help put things in perspective so that my (non-mathematical) mind can put things in perspective because, intuitively, I would have expected it to be much however but math is pretty definitive on the subjet (barring said issues).

The couple had moved from Michigan (w 14.6 unemployment) to Texas for jobs but found no jobs there. Then moved to Tennessee where an online friend was going to take them in but backed out at the last minute (in hindsight, probably for a reason). Someone paid them for a motel room but then had to leave to “go live w his girlfriend.” She and her 27 year old son needed a place to stay.

I was prepared to offer accomodations in my house. Had a pow wow with my trusted advisors/friends/employees and the vote was 4-0 that it was a scam (or worse).

The unemployment thing in Michigan was the math part. I was curious what the combined probability was. Of course, there were plenty of other red flags/concerns to make it a non-brainer. Still, the math part was very helpful in confirming the decision. (It was a loooong time ago before I took the combinations/permutations thingie in school so I was in the dark.)

Again, thanks! I don’t mind helping people in dire straights but the con artist/etc thing can really make one jaded. You all have earned your SD super hero capes!

edited: to resolve poor typing skills