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Probability of success in a binomial trial symbol?
The letter p, in lower case.
What does the Probability of success in a binomial trial symbol?
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.
What is the parameters that determine a Binomial Distribution?
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 an event has a 1 in 4 chance of occurring what is the probability of it happening to one individual in a sample of five?
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.
Does the probability of failure vary from trial to trial under binomial distribution?
No. It must remain the same.
