A spinner has four equal sectors, exactly one of which is red. It has just been spun four times and has stopped on red every time. What is the probability that the fifth spin also stops on red?

The spins are independent, so what has already happened cannot alter what the spinner does next: the fifth spin stops on red with probability 1/4, exactly as the first did. The value $1/1024=(1/4{)}^5$ is the probability of five reds in a row BEFORE any spinning starts; once four reds have already been seen, four of those five factors have been settled and only the last one is still uncertain. 'Red is due to stop' is the gambler's fallacy — a fair spinner keeps no account to settle, and the long-run balance is restored by later spins swamping the early ones, not by them being corrected. 'The spinner favours red' would be a fair suspicion about a spinner that might be biased, but the question states that the four sectors are equal, so the model is given and four spins is far too little evidence to overturn it.