Page 68 - Probability Demystified

CHAPTER 4 The Multiplication Rules 57

Independent and Dependent Events

The multiplication rules can be used to find the probability of two or more
events that occur in sequence. For example, we can find the probability of
selecting three jacks from a deck of cards on three sequential draws. Before
explaining the rules, it is necessary to differentiate between independent and
dependent events.
Two events, A and B, are said to be independent if the fact that event A
occurs does not affect the probability that event B occurs. For example, if a
coin is tossed and then a die is rolled, the outcome of the coin in no way
affects or changes the probability of the outcome of the die. Another
example would be selecting a card from a deck, replacing it, and
then selecting a second card from a deck. The outcome of the first card, as
long as it is replaced, has no effect on the probability of the outcome of the
second card.
On the other hand, when the occurrence of the first event in some way
changes the probability of the occurrence of the second event, the two events
are said to be dependent. For example, suppose a card is selected from a deck
and not replaced, and a second card is selected. In this case, the probability of
selecting any specific card on the first draw is 1 , but since this card is not
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replaced, the probability of selecting any other specific card on the second
draw is 1 , since there are only 51 cards left.
51
Another example would be parking in a no parking zone and getting a
parking ticket. Again, if you are legally parked, the chances of getting a
parking ticket are pretty close to zero (as long as the meter does not run out).
However, if you are illegally parked, your chances of getting a parking ticket
dramatically increase.

PRACTICE

Determine whether the two events are independent or dependent.

1. Tossing a coin and selecting a card from a deck
2. Driving on ice and having an accident
3. Drawing a ball from an urn, not replacing it, and then drawing a
second ball
4. Having a high I.Q. and having a large hat size
5. Tossing one coin and then tossing a second coin