I’m working my way through a book on mathematics and have come to a section on probability. I’ve not done probability before and whilst the resource has been excellent, in the word problems section of the text, it is using some terminology I can’t translate into anything I know.
The expression in context that’s confusing me issues is “This die has a probability of p of obtaining a six. Answer parts i-iii in terms of p.
What is this “probability p”?
(The question refers to an earlier situation I have analyzed and answered questions about by constructing a tree diagram. The situation is a dice game where three six sided dice are rolled simultaneously and points are awarded based on the number of 6s that show up with a points bonus if three 6s are rolled. I’ve included a picture of the tree).
Posting the questions relating to the word-problem with the unknown terminology here for further context, not seeking answers or strategies on them: i) Determine probability of rolling no sixes. ii) Determine therefore the probability of scoring points in a round iii) If the probability of scoring max points in a round is $1/27$, what is the value of $p$? iv) If the probability of obtaining exactly $16$ points in a round is $0.032$ while the probability of obtaining exactly $10$ points is $0.128$, determine the value of $p$.