02+Probability

Sections 2-6 and 14-3

A simple event is an event that consists of exactly one outcome.

Probability Of An Event
 * P(A) = || __The Number Of Ways Event A Can Occur__ ||
 * ^  || The total number Of Possible Outcomes ||

A simple example of this is flipping a coin. If you flip a fair coin one time, then there are two different possible outcomes (Head shows or Tail shows). Each outcome is equally likely since the coin is fair. Thus the probability of any one of the distinct outcomes (say "Heads showing") is 1/2 (1 divided by the total number of outcomes.) The total probability associated with the sample space is 1 (1/n added together n times). Yobani mathgoodies

__Mutually inclusive__: An event that can occur at the same time, such as the probability of pulling an ace __or__ a spade from a deck is inclusive because you can pull an ace that is a spade.

__Mutually exclusive__: An event that cannot occur at the same time, such as rolling a 2 __or__ 4 on a dice. It is not possible to roll a 2 and a 4 at the same time.

Quiz:

State if the example is exclusive or inclusive

1. Rolling a even number or a 2 on a die a. Exclusive b. Inclusive

2. Pulling a red card or a spade from a deck of cards a. Exclusive b. Inclusive

3. Rolling a 2 or an odd number on a die a. Exclusive b. Inclusive

4. Rolling a die and having it be 6 or a 1 a. Exclusive b. Inclusive

5. Picking a king or a spade out of a deck of cards a. Exclusive b. Inclusive

Answers: 1. Exclusive 2. Exclusive 3. Inclusive 4. Inclusive 5. Exclusive

Mutually Exclusive

14-3 Probability of Compound Events

INDEPENDENT AND DEPENDENT EVENTS- A single event, like snow on Saturday, is called a simple event. Suppose you wanted to determine the probability that it will snow both Saturday and Sunday. This is an example of a compound event, which is made up of two or more simple events. The weather on Saturday does not affect the weather on Sunday. These two events are called independent events because the outcome of one event does not affect the outcome of the other.

KEY CONCEPT PROBABILITY OF INDEPENDENT EVENTS-

EX: Words: If two events, A and B, are independent, then the probability of both events occurring is the A product of the probability of A and the probability of B.

Symbols: P(A and B)=P(A)P(B)

When the outcome of one event affects the outcome of another event, the events are dependent events. For example, drawing a card form a deck, not returning it, then drawing a second card are dependent events because the drawing of the second card is dependent on the drawing of the first card.

EX: A bag contains 8 red marbles, 12 blue marbles, 9 yellow marbles, and 11 green marbles. Three marbles are randomly drawn from the bag and not replaced. Find each probability if the marbles are drawn in the order indicated.

a. P(red, blue, green) The selection of the first marble affects the selection of the next marble since there is one less marble from which to choose. So, the events are dependent. First marble= P(red) 8/40= 1/5 Second marble= P(blue) 12/39= 4/13 Third marble= P(green) 11/38 The next step is to multiply each fraction which equals 44/2470 then you simplify leaving you with 22/1235. So, the probability of drawing red, blue, and green marbles is 22/1235

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