Imagine, if you will, you are flipping two coins in the air.

Each individual coin has a 50% chance of landing heads or tails—most people older than six know this—but what are the chances of getting an equal number of heads and tails when flipping both coins? 

With two coins, you have four possibilities: HH, TT, HT, or TH—therefore the probability of getting exactly one head and one tail is also 50%.

Expand the scenario to four coins being flipped in the air, and the probabilities change. Each coin still has an equal chance of being heads or tails, but the probability of getting exactly two heads and two tails is now only 38.7% (6 out of 16 possible combinations).

In other words, it’s now much more likely you’re NOT going to get an equal amount of heads and tails when you flip, even though statistically 2H and 2T will still be the most common individual result among all specific values of X heads and Y tails.

(Yes, I’m going somewhere with this…be patient)

Increase the number of coins flipped in the air further, and the discrepancy between equal and non-equal results becomes even more pronounced:

• 10 coins: A 24.6% chance of getting exactly 5 heads and 5 tails
• 100 coins: Only an 8% chance of getting 50 heads and 50 tails
• 1000 coins: Now we’re down to a 2.5% chance of getting exactly 500 heads and 500 tails.

(If you’re curious, the middle coefficient of Pascal’s Triangle is the key to calculating how likely flipping N coins will result in an equal number of heads and tails)

We can see that equal probabilities do not usually produce equal results when combined in groups…in fact it rarely occurs at any large volume.

If we were to take 1000 people and have them all flip a coin, then divide them into two groups according to whether they flipped heads or tails, 97% of the time we would NOT have an equal number of people in each group, despite the fact that each person started out with an entirely equal probability of being in either group in the first place.

Is this significant, other than as a bit of statistical trivia?   Perhaps, because it goes to show just how unlikely true ‘equality’ can be when you’re dealing with large volumes--such as, for example, human populations larger than a household.

Take a million men and a million women and have them choose between two occupations: engineer and teacher, and even if every individual component (ability, interest, and opportunity) were completely equalized between the genders, the likelihood that you’d end up with an equal number of men and women in each discipline is so statistically unlikely, it would be a modern-day miracle!

Turning to a doctrinal perspective: there have been a number of articles discussing the idea that “women are just more naturally spiritual than men”. This is somewhat of a non-starter, simply because “spirituality” is not easily measured or quantified.

(Although I believe there’s a lot of fairly substantial evidence that women in the Church are (a) more likely to attend church regularly and (b) more likely to have a temple recommend. I’ve also—anecdotally--never seen or heard of any area of the world where the number of active single men remotely equaled the number of active single women in any given ward or branch…)

This comes into play with the idea that there will be an equal number of men and women in the highest realm of the celestial kingdom. Sounds nice in theory, but look at the numbers: we’re talking about billions upon billions of spirit children from all of human history.

Even if we assumed the likelihood of each individual man and woman attaining celestial glory to be equal—say, flipping a coin: heads, you’re in, tails you’re out--the likelihood from a statistical standpoint that the ratio would be exactly 50/50 is vanishingly small, using the same mathematical calculation as above.   Add in any amount of difference between male and female exaltation rates—since it’s not really like flipping a coin, of course—and that exceedingly slim chance of true gender equality becomes even slimmer.

Now what? The problem, of course, is that in this instance, there’s no margin of error. If we counted those engineers from above and found there were 503,920 male engineers, and 496,080 female engineers, that would probably be ‘equal enough’ in most minds.   But there’s no ‘equal enough’ from an eternal family perspective, since each individual man needs to be paired with a woman (and vice versa). If the ratio between men and women is off by any amount at all (even one), that leaves you with some population of ‘single’ spirits with no possible mate.

If celestial sealing is necessary for exaltation, but we’re left with X number of single spirits of one gender or the other due to a (seemingly inevitable) imbalance, then how do we deal with it? There seems to be three primary possibilities:

1. The “P” word: No one wants to talk about the possibility of celestial polygamy, but if we presume any gender imbalance will probably be in ‘favor’ of the women, what other options are there?
2. “Affirmative Action”: Presuming, again, men are in the minority, in order to achieve gender equality, we’d have to ‘cheat’ and allow more men who would not normally be celestial-worthy to enter, simply to fill in the gap. While this situation eliminates the necessity for the ‘P’ word above, we now have a different problem—now, in essence, women are being judged by a higher standard than men. We would conceivably have situations where a man and a woman of equal ‘worthiness’ (however we define it) could receive unequal levels of glory, simply because of the comparative levels of righteousness from the other (completely unrelated) populations of the same gender. Would this be more or less unfair for women than option #1?  (Not to mention this would directly contradict D&C 88:22)
   
3. “Sorry, tough luck”: "...Rules are rules, and without a mate, you’re just not eligible for exaltation. Personal worthiness aside, you’ll just have to accept your fate on a lower tier of glory.  Um, sorry about that..."    Again, more or less fair than options #1 or #2?
   

Now, mind you, I haven’t the faintest idea what’s going to happen in the afterlife—there may be a dozen mitigating factors as yet unknown to us that influence the destiny of man- and womankind such that neither of the above solutions is necessary. 

(One possible “X Factor”: I believe it is statistically proven that male infants are more likely to die when they are very young compared to female infants. Since infants who die early are doctrinally destined to be 'celestialized', this would be one factor that might help counteract any gender imbalance based on adult spirits. Would God ‘cheat’ by arranging to bring home a certain number of young boys below the age of accountability—to the chagrin of their parents--if it served to balance out potential gender issues in the future? Who knows…)

Still, as we speculate about the future, we might need to temper our ideals with the statistical reality that according to cold, dispassionate mathematical equations, true 'equality' is very difficult to come by...