If you are tossing a fair coin 10 times what is the probabil

If you are tossing a fair coin 10 times, what is the probability of getting 4 OR 5 heads out of the 10 coin tosses? Please show work.

Solution

se the binomial formula:
Pr(X=x) = (n choose x) * p^x * (1-p)^(n-x)
where
x = number of successes
n = number of trials
p = probability of success

For this problem,
x = 5 heads
p = 0.5 chance of getting a head
n = 10 tosses

So:
Pr(X=5) = (10 choose 5) * (0.5^5) * (0.5^5)
= 0.246094

and

Pr(X=4) = (10 choose 4) * (0.5^4) * (0.5^6)
= 0.205078

so, required probability

Pr(4 0r 5 heads)= 0.246094 + 0.205078

=0.451172