Either/Or Probabilities

Question

If you toss four coins, what is the probability that you will get exactly 2 or 4 heads?

 

Compute the probability.

(Round to three decimal places.)

Answer 1

There are 2 possibilities for each coin, and each coin's result is independent -- so there are a total of 2⁴ = 16 different combination of events when tossing 4 coins.

 

How many ways can you get 2 heads?  That's ₄C₂ = 4! / 2!2! = 24 / 4 = 6.

 

How many ways can you get 4 heads.  That's ₄C₄ = 4!/ 4!1! = 1.  But it's also easy to figure that out without the formula.  There's only way to get 4 heads in 4 tosses, and that's for every one to come out heads.

 

So there are 7 different ways you can get 2 or 4 heads.  So the probability is 7/16 = 0.438