Suppose you flip a coin three times.

What is the probability of getting exactly one heads?

Assume that the coin is 'normal'.

Each flip produces 2 equi-probable outcomes; Heads or Tails. So three flips will produce 2^3 = 8 equi-probable sequences of outcomes.

These are:

1. H H H All three Heads
2. H H T Two Heads; One Tails
3. H T H Two Heads; One Tails
4. H T T One Heads; Two Tails
5. T H H Two Heads; One Tails
6. T H T One Heads; Two Tails
7. T T H One Heads; Two Tails
8. T T T All three Tails

These eight sequences are mutually exclusive and combinationally exhaustive. In exactly three (# 4,6,&7) out of these eight sequences, Heads appears exactly once.

Hence probability of getting exactly one Heads = 3/8 = 0.375

Posted by Sanjay on 2003-05-20 02:43:38