Back to Probability Theory

### Problem

- A coin is randomly flipped three times in a row; what’s the probability of three heads?
- Three coins are tossed simultaneously; what’s the probability of three heads?

### Solution

###### Three Heads in a Row

- The branches of the
*Possibility Tree*represent the eight possible outcomes of flipping a coin three times, the rightmost branch representing three heads. Thus the probability of tossing three heads is 1/8, one branch of eight.

- The possibilities can also be listed in a
*Possibility Table*:

- Rows in the table correspond to branches in the tree.

- Finally, the probability can be computed using the Special Conjunction Rule (SCR):
**P(A&B) = P(A) x P(B)**, where A and B are independent, i.e. where the truth of one doesn’t affect the probability of the other.

- Thus the probability of three heads is:
**P(H1 & H2 & H3) = P(H1) x P(H2) x P(H3) = ½ x ½ x ½ = ⅛**

###### Three Heads Simultaneously

- Tossing three coins simultaneously is logically analogous to tossing one coin three times, the situations differing in no way affecting their probabilities. The probability is thus ⅛.
*Argument by Analogy*is useful in calculating probabilities in complex situations: think up a simpler, logically analogous scenario and calculate the corresponding probability.