Although It Hard To Be Definitive In Classifying

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Although it’s hard to be definitive in classifying people as right- or left-handed, some studies suggest that about 14% of people are left-handed. Since 0.14 × 0.14 = 0.0196, the Multiplication Rule might suggest that there’s about a 2% chance that a brother and a sister are both lefties. What’s wrong with that reasoning?

Answer: Events are not independent.

Explanation

The events have to be independent to be able to use the multiplication rule, meaning that the probability of being left-handed has to be independent for brother and sister.

However, these events are not independent, because the probability of a brother and sister being left-handed will be higher than the probability of two unrelated people being left-handed (Think for example of twins).

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