I am sure you are correct
As someone with a background in financial mathematics, probability and statistics is not my main specialty, but if my memory on probability serves me correct, then this is the (correct) justification:
Probabillity is divided into independent and dependent events. Independent events are generally easier to deal with.
So picture the 152 AUT-63 drug packages being placed in a non-see through bag. With 50% chance of a placebo, 76 of them are AUT-63, 76 of them are placebo. Agree? You are blind-folded as you choose the 4 of the 152 drug packages in order to make the selection unbiased.
In the above scenario with a 50% probability of each event, the selection process is like flipping an unbiased coin. Heads or tails... 50% chance of either event. What is the chance of flipping 4 tails in "one go" (i.e. one after the other). Well, the probablility is:
P(T)*P(T)*P(T)*P(T) = (1/2)*(1/2)*(1/2)*(1/2) = 6.3%
The probability of "all other events" is therefore 1 - 0.063 = 0.937 = 93.7%
"All other events" includes just 1 person ending up with AUT-63, 2 people with AUT-63, 3 people with AUT-63 and 4 people with AUT-63. So the chance of at least one person (out of the 4 enrollments) ending up with the drug is 94%...
The above assumes an independent selection event (i.e. with replacement of each drug package to the bag after it has been drawn). In reality it is not an independent selection as each participant holds on to the drugs package after they have received it (i.e. a dependent event). So...
P(placebo 1st draw)*P(placebo 2nd draw)*P(placebo 3rd draw)*P(placebo 4th draw) = (76/152)*(75/151)*(74/150)*(73/149) = 6.002%.
Because the selection is being done from a large number of packages, dependent events can be approximated by independent events (in this case; not so when selecting from a small sample e.g. "10"). You can calculate the difference in the approximation by...
P(independent) - P(dependent) = 6.250% - 6.002% = 0.248% (this is the error involved with the assumption - i.e. "small").
And that's stretching my memory a little...