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A family of five plans to go together either to the beach or to the mountains, and a coin is tossed to decide.

We want to know the number of people going to the mountains.

When this experiment is viewed as composed of five binomial trials, one for each member of the family, the outcomes of the trials are obviously not independent.

Indeed, the experiment is better viewed as consisting of one binomial trial for the entire family.

The following is a less extreme example of dependence.

Consider couples visiting an art museum.

Each person votes for one of a pair of pictures to receive a popular prize.

Voting for one picture may be called `` success '', for the other `` failure ''.

An experiment consists of the voting of one couple, or two trials.

In repetitions of the experiment from couple to couple, the votes of the two persons in a couple probably agree more often than independence would imply, because couples who visit the museum together are more likely to have similar tastes than are a random pair of people drawn from the entire population of visitors.

Table 7-1 illustrates the point.

The table shows that 0.6 of the boys and 0.6 of the girls vote for picture A.

Therefore, under independent voting, Af or 0.36 of the couples would cast two votes for picture A, and Af or 0.16 would cast two votes for picture B.

Thus in independent voting, Af or 0.52 of the couples would agree.

But Table 7-1 shows that Af or 0.70 agree, too many for independent voting.