Weights on the two coin spaces

Topic: Random experiments and probability · more questions on this topic
‹ Three coin tosses Drawing from 365 balls ›

A fair coin is tossed three times, and the tosses are independent. Assign a probability to every outcome of each of these two sample spaces: the set of sequences in \{0,1\}^3, and the set \{0,1,2,3\} of possible numbers of heads.

  1. Independence and fairness give probability 1/8 to each of the eight sequences.

  2. The number of heads is binomial. \mathbb{P}(\{0\})=\mathbb{P}(\{3\})=1/8 and \mathbb{P}(\{1\})=\mathbb{P}(\{2\})=3/8.