EXAMPLE 3 Investigating independence

Suppose we tossed a fair coin 15 times and obtained the following sequence of outcomes:

Toss: 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15
Outcome: H H H T H H T T T T T H H T T

451

For the first 14 tosses, the following toss is the same nine times. The proportion of times a toss is followed by the same outcome is

proportion

For so few tosses, this would not be considered a large departure from 0.5.