Final answer:
The Alabama paradox does not occur when increasing the number of judges from 300 to 301 because the conditions described relate to binomial probability, not the apportionment method known as the Hamiltonian method.
Step-by-step explanation:
The Alabama paradox refers to a situation that arises in the apportionment process used in allocating seats in a legislative body, specifically when using the Hamiltonian method.
This paradox occurs when an increase in the total number of seats causes a state to receive fewer seats than before the increase. In the context presented, increasing the number of judges from 300 to 301 and applying the criteria mentioned (fixed number of trials, two possible outcomes, and independent trials conducted under identical conditions) would not result in the Alabama paradox.
This is because the criteria given actually describe the characteristics of a binomial probability distribution, not the conditions for the Hamiltonian method. Therefore, an increase in the total number of judges would not lead to the Alabama paradox under such conditions.