Am trying to calculate the odds of my wife and I getting pregnant

[jskosmo]

I'm totally not a math guy - registered for this forum just for your help. Thank you for reading!

OK - my wife and I are about to embark on the most expensive of procedures to try and get pregnant. We can pay per procedure, or we can pay a fixed price of $25,000 (insurance of sorts) that covers everything, and we get 70% of our money back if we don't take a baby home (seriously).

We're trying to figure out which way to go.

Here's the problem:
1) First procedure - $12,000 (called a 'fresh cycle') - probability of pregnancy is 40%
2) Second procedure - $3,000 (called a 'frozen cycle') - probability of pregnancy is 25%
3) Third procedure - $12,000 (another fresh cycle) - probability of pregnancy 40%
4) Fourth procedure - $3,000 (another frozen cycle) - probability of pregnancy is 25%
5) Fifth procedure - $12,000 (another fresh cycle) - probability of pregnancy 40%
6) Sixth procedure - $3,000 (another frozen cycle) - probability of pregnancy 25%
After the six procedures - if we don't get pregnant, then we get 70% of the $25,000 back - which we'd probably use to adopt (the doctors say we've hit the point of diminishing returns).

On top of all this - the probability of a miscarriage is always 22% (in each scenario above). It can drop if we implant multiple embryos, but let's assume worst-case (22%).

We're pretty 'normal' - no conditions or issues that would cause us to deviate from the probabilities above.

We can go without 'baby insurance' - in which case we pay per procedure until we get pregnant (which could get really expensive - and might end up with lots of cost but no pregnancy at all) - or we can go with insurance - $25,000 and 70% back if we don't take home a baby (not just get pregnant - take home a baby). Medications are expensive, but those are the same cost in either case, so am not figuring that into this.

Honestly - I'm not even entirely sure how to go at this.
I think I'd like to figure out:
- The amount we'll likely spend getting pregnant 'going it without insurance' - then I'll compare this against $25,000 and figure out which is a better deal.
- What's the probability of 'going it alone' and going through all six steps above, and ending in no pregnancy?
- Would probably like to know the probability of pregnancy after each of the six steps above.

But if you can recommend a different way to go at this, I'd be grateful.

Thanks for any and all input!

 

[bpet]

This all hinges on your spending strategy, whether or not the success probabilities of each procedure are independent (i.e. if the first two rounds are failed does that change the chance in the next two rounds), and how accurate/correct is the information they provided.

Assuming the probabilities are independent and accurate, then after the first two rounds you've got 75% of 60% chance (i.e. 45% altogether) of having spent $15k for nothing. Including the miscarriage chance would increase that a bit, say about 50-50 chance you'd have a baby after spending $15k. If failing the first two rounds doesn't change your chances in the next two, then you've got another 50-50 chance of a baby after spending another $15k, i.e. 25% chance of spending $30k for nothing. Similarly if your budget is unlimited then eventual success is almost guaranteed.

On the other hand with the insurance option there's a 40% chance that you spent $25k when it could have cost $12k, but your maximum spend is capped.

Hope this helps, though it shouldn't take the place of independent legal & financial advice. Good luck!

 

[CRGreathouse]

Assuming independent probabilities (not true, but probably 'close enough'), with cumulative probabilities in parentheses:

Without insurance:
Success @ $12,000: 31.2%
Success @ $15,000: 13.4% (44.6%)
Success @ $27,000: 17.3% (61.9%)
Success @ $30,000: 7.4% (69.3%)
Success @ $42,000: 9.6% (78.9%)
Success @ $45,000: 4.1% (83.0%)
Failure @ $45,000: 17.0%
Expected cost: $26,167

With insurance:
Success @ $25,000: 83.0%
Failure @ $7,500: 17.0%
Expected cost: $22,027

So the insurance seems like a good call.

 

[HallsofIvy]

The odds of you getting pregnant are probably 0!

 

[bpet]

So the insurance seems like a good call.

Another option would be to take the first 1 or 2 procedures and go straight to adoption if they fail, then the expected cost is under $15k (not counting the adoption cost).

Also these calculations are sensitive to the probabilities and since they are given as nice round numbers there could be a significant amount of uncertainty. If the true probabilities are lower then it makes the insurance more favourable. Otherwise the non-insurance option could become more favourable, if expected cost is the only decision factor.

I think the strategy to choose all depends on your risk aversity. A risk-taking strategy is $12k for about 1 in 3 chance at success and 2 in 3 chance of having to spend more to either continue or adopt; in the middle it's $25k for about 5 in 6 chance of success and 1 in 6 chance of having to adopt; at the risk-averse end for some fixed smaller cost you'd go straight to adoption.

Tough decision.

 

[CFDFEAGURU]

But if you can recommend a different way to go at this, I'd be grateful.

All I did was poke and hope.

Sorry, I couldn't help it.

LOL

Thanks
Matt

 

[jskosmo]

Thanks so much - we're grateful for your input (and humor).

This is a huge decision (the whole deal - over and above the insurance part) - you've helped us tremendously.

I think we've chosen to go no insurance and a limited number of procedures - the procedures are not fun (lots of shots in fun places for weeks).

Thanks again to all of you. Best wishes.