Calculation for the frog riddle

Consider 1000 cases of this problem.  As the video says, there are 4 possible combinations (MM, MF, FM, FF)  and so each will occur about 250 times.  Suppose the probability that a given male croaks in the time interval in question is a small probability "p".  Then in the case there are two males, the probability that one croaks is about 2p.  We need to count the number of cases in which we hear a male croak (this is the "information" we have) 

(cases with FF)  250 times 0 = 0
(cases with MF) 250 times p = 250 p
(cases with FM) 250 times p = 250 p
(cases with MM) 250 times 2p = 500 p

So the total number of cases in which we would hear a male croak is 1000 p. Of these, about 500p cases lead to survival and the other 500p to death. In other words, about 50% of cases lead to survival.

This is a good demonstration of why one should use expected frequencies when teaching elementary probability.