Question

You flip a fair coin 5 times, what's the probability of getting 4 or 5 heads?

Answer 1

31/32

Answer 2

Recall the binomial distribution:
\[\large P(X=x)={n\choose x}p^x(1-p)^{n-x}\]
You want P(4 or 5). By the addition rule, you have P(4 or 5)=P(4) + P(5)
\[\large P(X=4)={5\choose 4}\left( \frac{1}{2}\right)^4\left(1- \frac{1}{2}\right)^{5-4}\\
\large P(X=5)={5\choose 5}\left( \frac{1}{2}\right)^5\left(1- \frac{1}{2}\right)^{5-5} \]
Then:
the total probability is \(P(X=4)+P(X=5)\)

Answer 3

31/32 seems like a really high probability.. I would find it hard to believe that you're almost certain to observe 4 or 5 heads. How did you get that number?