IVF baby probability? We have two embryos.  Our IVF doc said the probability of success implanting a single embryo is 40% whereas the probability of having one baby with implanting two embryos at once is 75% (with a 30% chance of twins).
What is the chance of having at least one child if we implant the embryos one at a time?
My calculation is 1- (chance of failure twice in a row)= 1 - 0.6*0.6 = 64%.  Is this correct?  Does it underestimate our chances since we would stop if the first was a success?
Thanks.
 A: No.  The probability of having 1 success when you attempt the procedure at most twice, but stop on the first success, is the same as the probability of having at least 1 success when you perform the procedure twice whatever the result of the first try.
If you stop when the first trial is successful, then the probability of a success is: $$0.4 + 0.6\cdot 0.4 = 0.64$$
If you perform both trials reguardless of the result of the first, then the probability of at least one success is: $$0.4\cdot0.4 + 0.4\cdot 0.6 + 0.6\cdot 0.4 = 0.64$$
Which is also $1-0.6\cdot 0.6 =0.64$ in both cases.
All stopping on the first success affects is the probability of having two successes.  Obv.

PS: This is assuming that the attempts are independent.   That the result of having tried the procedure once before does not affect the probability of success on a second trial.   This may not be the case.
A: For the 1st specific question, I would agree with your combined probability of 64% for one or more children after 2 independent single embryo implants.
For your 2nd question, the 2nd implant is no longer independent from the results of the 1st implant.  Therefore, you want to list all 3 possible outcome states, and calculate probabilities for each:
   baby on first implant then stop:  .40
   first implant fails, 2nd one succeeds:  .60 x .40 = .24
   both implants fail:  .60 x .60 = .36
Now, combine the two outcomes where you get one success, .40 + .24 = .64
Even tho you're comparing two different scenarios, the probabilities for them are the same.  In the first scenario, you could end up with 2 successful pregnancies, and in the 2nd scenario, the most you can end up with is one. Isn't choice great?
