You flip a fair coin 45 times, and your friend flips a fair coin 55 times. What is the probability that you get at least as many heads as your friend does?
This is a problem on my homework and I have no idea how to solve it. My first thought was to use normal distributions, but I don't know how to do this.
Guide:
You can model the number of heads as Binomial distribution, and you are interested in their difference. Since you mentioned normal distribution, yes, we can use normal distribution to approximate Binomial distributions.
$X \sim Bin(45, 0.5)$, $Y \sim Bin(55,0.5)$, compute the mean and variance of $X-Y$ and approximate it using a normal distribution.