 Statistical Independence

Two events, A and B, are independent if the fact that A occurs does not affect the probability of B occurring.

Examples:
• A tossed coin lands on heads AND a rolled die comes up a 6.
(tossing coins is not dependent on what happens with a die!)
• A red marble is drawn from a jar AND a card chosen from a deck of cards is an ace.
(Choosing marbles from a jar is not dependent on what's selected from a deck of cards)
• A card drawn from a deck of cards is an ace and, after replacing the card in the deck, a second card drawn from the same deck is also an ace.
(Since the card was put back the number of aces in the deck for the second draw is the same as the first draw).
• A red marble is drawn from a jar and then, after the marble is put back in the jar, another red marble is chosen from the same jar.
(Since the marble was put back in the jar, the second draw has the same probability as the first draw).
Two events, A and B, are dependent if what happens on B depends on what happened with A.

Examples:
• A card drawn from a deck of cards is an ace and a second card drawn from the same deck (without replacing the first card) is also an ace.
(Since the first event lessens the number of aces in the deck (there are only 3 now), the probability of drawing a second ace is now affected (it is lower).
• A red marble is drawn from a jar and then another red marble is chosen from the same jar while the first marble is not replaced before the second draw.
(Since the first event lessens the number of red marbles in the jar the probability of drawing a second red marble (or any color marble for that matter) is affected (it is lower).