# Calculating a probability for an individual not selected

I just had my first lecture in statistics and we were left with a question before the class ended, and I have no idea how to solve it.

The question goes: Every day at training camp there will be a drawing of lots to figure out, who has to do the dishes. Every day there will be 4 people doing the dishes and there is a total of 35 people. The possibility of getting chosen is equal for everybody, every day. Calculate the probability that a random person will NOT be chosen during the entire camp, which lasts for 7 days.

I have no idea what to search for on Google, so if anyone can guide me to either the solution or a link, it would be much appreciated.

Thank you.

• I suspect several thousand posts on this site answer some variant of this question. Here's a search that turns up some: stats.stackexchange.com/search?q=probability+not+self-study.
– whuber
Dec 8, 2017 at 17:28
• Does your teacher expect you to solve this problem after one lecture and a Google search? Dec 8, 2017 at 20:23

(I hope that by "a random person", you mean a given person. Otherwise, I have no idea what the problem is asking.)

Suppose the person's name is Bob. Try splitting the problem into the following steps.

1. On day 1, what's the probability that Bob is chosen?
2. On day 1, what's the probability that Bob isn't chosen?
3. What's the probability that, every day Bob is at the camp, he isn't chosen?