TITLE: If five coins are flipped simultaneously, find the probability of each of the following:
QUESTION [7 upvotes]: If five coins are flipped simultaneously, find the probability of each of the following:
(a) At least one coin lands heads;

My answer:$\frac{2^5 -1}{2^5}$. I took the complement for the numerator.

(b) At most one coin lands heads.

My answer: $\frac{6}{2^5}$. I counted how many times heads appears $1$ or $0$ times.
Is this correct?

REPLY [4 votes]: Good job!!
For part a, notice that this is the OPPOSITE of (no coin lands heads <=> all coins land tails), which is $\displaystyle \left(\frac12 \right)^5=\frac{1}{32}$ chance.
For part b, any $5$ of the coins can land heads, if in total one coin lands heads. If no coin lands heads, that can be done in $1$ way. That is $\displaystyle \frac{6}{32}=\frac{3}{16}$ chance.
In general, take a look at the binomial distribution.