Probalities: X rule

Probalities: X rule

1. ·

   • Two events are independent if whether one happens has absolutely no influence on whether the other happens.
     • knowing about the outcome of one event gives absolutely no information about how the other event will turn out.
       • If I tell you I rolled two dice, and the first die was a 4, then knowing that give you no clue about what the number on the other die might be.
         • If I shuffle a deck of cards, draw one, replace it, re-shuffle, and draw another, then the two cards are independent.
           • If events A and B are independent
             • Special AND rule
               • P(A and B) = P(A)*P(B)
         • If three women are randomly selected
   • BUT, if I shuffle the deck, draw one card, and then without replacement draw a second card, then they are not independent.
     • if the first card is the 7 of Hearts, then it is less likely that the second card would be either a 7 or a Heart, because there are fewer of those options among the remaining 51 cards.

2. “AND” means MULTIPLY