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.