Assume that Tom attends randomly with probability 0.55 and that each decision is independent of previous attendance. What is the probability that he attends at least 7 of 10 classes given that he attends at least 2 but not all 10 classes?
1 Answer
I got
Explanation:
Let's first work on the binomial probability of Tom attending his classes.
We'll be using this relation:
Looking at the full range of probabilities for Tom attending class, we'll have
So now let's get more into the specifics. We're looking for the probability that he attends class, but it's a conditional probability - we're told he attends at least 2 but not all 10 - which means the probability of his attending "all his classes" isn't 1 but something less than that - we need to subtract out the classes we know he won't attend and set that as the denominator:
Now the numerator. We're asked for the probability that he attend at least 7 of his classes, but we're also told he won't attend all 10, and so we'll sum up for
And so the probability that he attends at least 7 classes, knowing he'll attend at least 2 but not 10 is: