 Extending our previous terminology, we shall say that a true bias value \(p\) is for a hypothesis H if it lies within the set specified by \(H\). In our example, a bias value p is correct for \(H_1\) if and only if \(p = 0.5\); otherwise \(p\) is correct for \(H_2\). Given a true bias value \(p\), and assuming independence, we can compute a probability for any finite sequence of observations. This probability is known as the sample distribution. For example, for a fair coin with \(p = 0.5,\) the probability of observing 3 heads is \(0.5 \times 0.5 \times 0.5 = 0.125.\) If the chance of heads is 0.7, the probability of observing 3 heads is \(0.7 \times 0.7 \times 0.7 = 0.343.\) Notice how the independence assumption allows us to compute the probability of a sequence of observations as the product of single observation probabilities. Without the independence assumption, we cannot infer the probability of multiple observations from the probability of a single observation, and the sample distribution is not defined. 