Independence is a more strict condition. The probabilities must follow the rule<p>P(A and B) = P(A) * P(B)<p>that is the rule that is used in the article.<p>Let&#x27;s pick an easier example. You buy two equal decks of cards while traveling abroad. When you return home, you realize that it may be a deck with 48 cards (123456789JQK)or a deck with only 40 cards (1234567JQK) without the &quot;8&quot; and &quot;9&quot;.<p>To make it simple, suppose that you magically know that you have a 50% chance of having bought a 48 cards deck and a 50% chance of having bought a 40 cards deck.<p>One of your friend come and start to shuffle both decks, one in each hand, without mixing them.<p>If your friend picks a card from the right deck, what is the probability that it&#x27;s a &quot;8&quot;? (spoiler alert: There is a 50% that the deck has only 40 cards (without the &quot;8&quot; and &quot;9&quot;) and you can&#x27;t pick the &quot;8&quot;, and there is a 50% that the deck has 48 cards and there is a 1&#x2F;12 to pick the &quot;8&quot;, so the probability is: 1&#x2F;2 * 0 + 1&#x2F;2 * 1&#x2F;12 = 1&#x2F;24)<p>If your friend picks a card from the left deck, what is the probability that it&#x27;s a &quot;8&quot;? (again 1&#x2F;24)<p>Are they independent? Whatever he does with the left decks doesn&#x27;t affect the right deck. To get less relation, you can use two friends, and put them in a different room, and make them pick the card exactly simultaneously.<p>If the events were independent, the probability that both have picked an &quot;8&quot; would be 1&#x2F;24 * 1&#x2F;24 = 1&#x2F;576<p>But the correct answer is more complicated. There is a 50% that the deck has only 40 cards (without the &quot;8&quot; and &quot;9&quot;) and you can&#x27;t pick the &quot;8&quot;, and there is a 50% that the deck has 48 cards and there is a 1&#x2F;12 to pick the &quot;8&quot; in each one, so the probability is: 1&#x2F;2 * 0 + 1&#x2F;2 * 1&#x2F;12 * 1&#x2F;12 = 1&#x2F;288. That is 2x bigger than if they were independent.