Description

The die coin experiment consists of rolling a die and then tossing a coin the number of times shown on the die. Random variable \(N\) gives the die score and random variable \(Y\) gives the number of heads. The probability of heads \(p\) for the coin can be varied with a scrollbar. The die distribution can be chosen with the drop-down box. The following choices are available:

• fair: each face has probability \(1 / 6\).
• 1-6 flat: faces 1 and 6 have probability \(1 / 4\) each; faces 2, 3, 4, and 5 have probability \(1 / 8\) each.
• 2-5 flat: faces 2 and 5 have probability \(1 / 4\) each; faces 1, 3, 4, and 6 have probability \(1 / 8\) each.
• 3-4 flat: faces 3 and 4 have probability \(1 / 4\) each; faces 1, 2, 5, and 6 have probability \(1 / 8\) each.
• skewed left: face \(i\) has probability \(i / 21\) for \(i \in \{1, 2, 3, 4, 5, 6\}\).
• skewed right: face \(i\) has probability \((7 - i) / 21\) for \(i \in \{1, 2, 3, 4, 5, 6\}\).

Random variables \(N\) and \(Y\) are recorded in the data table, and their distributions described in the distribution graphs and tables. This experiment illustrates conditional probability and conditional distributions.