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In a jury of 12 people, it’s not likely that many will understand probability. In fact, it’s fairly likely that no one on a jury will have much grasp of probability.

People who have not studied probability nevertheless have some intuitive sense of probability, but they need help relating their intuitive sense to numbers and calculations. They need someone to relate numbers in unfamiliar settings to numbers in more familiar settings. They also need a guide to avoid misunderstandings.

Probability is subtle, and even people who are trained in math can fall into common errors. Two of the most common errors are (1) wrongly assuming independence and (2) getting conditional probabilities backward.

When two events are independent, the probability of both happening is simply the product of the probability of each happening separately. For example, if you flip a fair coin, there is a 1/2 probability of the coin coming up heads. And if you roll a standard die, there’s a 1/6 probability that you’ll roll a six. Assuming there’s no way for the coin flip and the die roll to influence each other, the probability of the coin coming up heads and the die coming up six is simply 1/2 × 1/6 = 1/12.

Independence is attractive because it is easy to compute, but it is not always appropriate. For example, if there’s a 30% chance of rain today and a 40% chance of rain tomorrow, you can’t assume there’s a 12% chance that it will rain both days. The weather on one day tells you something of what to expect the next day. Weather forecasts for consecutive days are not independent.

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