In typical notation, "p" is the probability of sucess and "q" is the probability of failure. So q = 1 - p. But for your question: p = p.
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The symbol for probability of success in a binomial trial is the letter p. It is the symbol used for probability in all statistical testing.
The letter p, in lower case.
The binomial distribution has two parameter, denoted by n and p. n is the number of trials. p is the constant probability of "success" at each trial.
If we assume that the probability of an event occurring is 1 in 4 and that the event occurs to each individual independently, then the probability of the event occurring to one individual is 0.3955. In order to find this probability, we can make a random variable X which follows a Binomial distribution with 5 trials and probability of success 0.25. This makes sense because each trial is independent, the probability of success stays constant for each trial, and there are only two outcomes for each trial. Now you can find the probability by plugging into the probability mass function of the binomial distribution.
No. It must remain the same.