Probability: If we flip a coin 5 times, what is the probabil

[mathlgs]

Question: If we flip a coin 5 times, what is the probability that the number of heads is an even number?

I know that it is divisible by 2 but not to sure where to go from there.

Thanks

 

[galactus]

When you flip a coin 5 times there are $\displaystyle 2^{5}=32$ different arrangements.

Of these, how many times does an even number of heads, that is, 2 heads or 4 heads appear?.

We flip 5 times and get 2 heads in $\displaystyle \frac{5!}{3!2!}=10$ ways

We flip 5 times and get 4 heads in $\displaystyle \frac{5!}{4!}=5$ ways.

$\displaystyle \frac{15}{32}$