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

#### MarkFL

##### Pessimist Singularitarian
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:

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

• anemone, karush and MarkFL

#### karush

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

ummm where does 8 come from??

#### MarkFL

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

• karush and anemone

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

#### karush

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