# Expected value for the total number of points awarded on any toss of coins

#### karush

##### Well-known member

well not sure why we need 3 different coins other than confusion
also each toss at least 2 coins have to have the same face
frankly not sure how any of these choices work
didn't want to surf online better to stumble thru it here and learn it better

#### MarkFL

Staff member
I would begin by listing the outcomes and their probabilities:

0 points: 1/8

3 points: 3/8

6 points: 3/8

9 points: 1/8

Then the expected value is the sum of the products of the points and probabilities associated with each outcome:

$$\displaystyle E[X]=0\cdot\frac{1}{8}+3\cdot\frac{3}{8}+6\cdot\frac{3}{8}+9\cdot\frac{1}{8}=\frac{9+18+9}{8}=\frac{9}{2}$$

#### karush

##### Well-known member
oh I see
it's basically a series...

ummm where does 8 come from??

#### MarkFL

Staff member
Each coin has two possibilities, either heads or tails, and since there are 3 coins, the total number of outcomes is $$2^3=8$$.

oh..

#### HallsofIvy

##### Well-known member
MHB Math Helper
Those 2^3= 8 outcomes are
HHH (worth 3(3)= 9 points)
HHT (worth 2(3)= 6 points)
HTH (woth 2(3)= 6 points)
HTT (worth 1(3)= 3 points)
THH (worth 2(3)= 6 points)
THT (worth 1(3)= 3 points)
TTH (worth 1(3)= 3 points)
TTT (worth 0(3)= 0 points)

#### karush

##### Well-known member
I'm very weak on this probability stuff
So the help was appreciated much