If sam joe and debbie each flip a coin how many possible out comes are there?

Answer 1

Three people flip a coin and there are two possible outcome of a coin flip.

(Except in one of my favorite Twilight Zone episodes which begins: Mr. Hector B. Poole, resident of the Twilight Zone. Flip a coin and keep flipping it. What are the odds? Half the time it will come up heads, half the time tails. But in one freakish chance in a million, it'll land on its edge. Mr. Hector B. Poole, a bright human coin, on his way to the bank.)

Since we are not in The Twilight Zone, here is one way to see this.

Sam has two possible outcomes, Joe has two more possible out come, so that is 4 and Debbie has two more so that is 8. So there are 8 possible outcomes. This is 23 .

In case you want to see them, here are all the possible outcomes:

1.head head head

2.head head tail

3.head tail head

4.tail head head

5.tail tail head

6.head tail tail

7.tail head tail

8.tail tail tail

When there are just two possible outcomes with fixed probability ( 1/2 and 1/2 in this case) summing to one. These distributions are called are called binomial distributions.

In this case, it is 3C0+3C1+3C2+3C3=1+3+3+1=8 where 3CN is the number of ways to choose N things from 3. Note that this is also the 4th row in Pascals triangle.