Question

You toss 5 coins. What is the probability that all 5 show heads?

Answer 1

Each event gets multiplied to the others, giving you
`(1/2)(1/2)(1/2)(1/2)(1/2)=1/32`

Explanation:

When we flip a coin, there is a 1 in 2 chance it will be heads.

When we flip 5 coins, each coin has a 1 in 2 chance of being heads.

So we have 5 halves. The question I often run into is "Should I multiply or should I add?" We can look at this 2 ways - one way is to say that when you have independent events, they will generally multiply. The other way to look at it is to go ahead and do both operations - multiply and add - and see which answer makes sense.

Let's do that - with multiplication:

`(1/2)(1/2)(1/2)(1/2)(1/2)=1/32`

and this makes sense - we have only 1 case (the numerator) where we have all heads out of 32 possible cases.

Now lets' do it with addition:

`(1/2)+(1/2)+(1/2)+(1/2)+(1/2)=5/2` - this says there are 5 cases out of 2 where only heads comes up. Clearly not what is going on!