



 
Hi, For a Binomial distribution you have an experiment (trial) with two possible outcomes, sometimes called success and failure. Your experiment is answering a question and success is getting the correct answer. The experiment is repeated $n$ times independently (in your case $n = 8$). In each trial the probability of success is the same (usually called $p$). The random variable $X$ is the number of success in the $n$ trials. Since Mr. Saul is guessing on each question and there are 4 possible answers with only one correct, on each trial the probability of success is $p = \large \frac{1}{4}.$ Hence in this case the random variable $X$ has a Binomial distribution. In the more general case described in 1) the probability of success might not be the same for each question. If the person taking the quiz is a sports fanatic then they will likely have a higher probability of getting a sports question correct than a history question. For the remainder of the questions you sent I suggest you go to the Quandaries and Queries page and use the Quick Search to search for the term binomial distribution. You will see our responses to a number of questions we have received and hopefully these responses will help. Penny 



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