Let's say we are organizing a dinner with $20$ guests. Every guests after his arrival he wants to eat pizza with probability $p=0.6$ and spaghetti with probability $1-p=0.4$, independetely from the others. So there is no time consumption, the host of the dinner decides to order earlier $16$ pizzas and $12$ spaghetti. What's the probability that not all guests can eat the food they prefer?
So, i guess this problem has to do with Bernoulli distribution or binomial distribution. I also guess we need to start from calculating the probability($P_A$) of that all guest will eat food of their preference and then to find the requested probability($P_B$) we will just do $P_B=1-P_A$. Maybe, having $20$ guests means that we cast an experiment $20$ times and and we consider that if a guest eats pizza, the experiment is succesful with the given probability $p=0.6$ (All these are just my assumptions)
Any hints on how to start?
If $X$ denotes the number of guests that go for a pizza then all guests can eat the food they prefer iff: $$8\leq X\leq 16$$
So the probability of this event equals: $$\mathsf P(8\leq X\leq 16)$$ where $X$ has binomial distribution with parameters $n=20$ and $p=0.6$.