Statistics - expected number Suppose the probability of success obtaining heads is $0.5$, number of trials $n=10$. In a class of $100$ students, each student tosses a coin (assumed fair) $10$ times. Write down the expected number of students who will obtain $0,1,\ldots , 10$ heads.
If I start with $0$ heads, I understand that I need to calculate the probability of $0$ students obtaining $0$ heads, then the probability of $1$ student obtaining $0$ heads and so on until $100$. Then multiply the probability by the number of students and add all $100$ cases to get the expected number. Now obviously this is a lot of work, and this is just a part of a question, so is there something I don't understand or know, or is it the question?

What's the probability that a student gets $0$ head? Suppose it's $A$.
Then the expected number of students who get $0$ head would be $100\times A$ since the probability of getting $0$ head is the same for all students.
