Probability

Probability Ex. 39, 40, 41

Probability is the measure of how an event is. In other words,

P (A) = n(A)        ®      Probability = Number of Favorable outcomes

                 n                                                   Total Possible Outcomes

Probability of event A is the number of ways event A can happen, divided by the total possible outcomes.

Sample Space is the complete set of all possible outcomes.

Ex.  Rolling a die, the sample space would be 1,2,3,4,5,6

Sample Spaces can be represented using tree diagrams or charts.

Addition Law (Or)           

When 2 events, A and B are mutually exclusive. The probability that A or B will take place is the sum of both events.

P (A or B) = P (A) + P (B)

Ex. A single 6-sided die is rolled. What is the probability of rolling a 2 or a 5?

P (2)	=	1
		6

P(5)	=	1
		6

P(2 or 5)

=

P (2)

+

P (5)

=	1	+	1
	6		6

=	2
	6

1

3 Mutually Exclusive- if the occurrence of one will mean that the other will not occur (Cannot have 2 events taking place at the same time). Mutually exclusive events add up to one (complement).  Ex. Venn Diagram, the circles do not overlap Non-Mutually Exclusive- if they have one or more outcomes in common Independent events - If the result of the first draw/event does not affect the outcome of the second draw/events. Ex. Event A – Drawing a card from a deck. Then returning the card in the deck. Event B – Drawing from the very same cards. Dependent Events-  when you don’t replace the first item before drawing the second item. Ex. What is the probability of getting a face card and then an Ace without replacing the face card? P (Face) = 12/52 P (Ace after Face) = 4/51 (12/52)(4/51) = 4/221 Multiplication Law (And) When 2 events, A and B are dependent and influence one another.  P (A&B) = P (A)P (B|A) You would read P (B|A) as “the probability of B given A has already occurred”, also known as, conditional probability. Ex. A jar contains black and white marbles. Two marbles are chosen without replacement. The probability of selecting a black marble and then a white marble is 0.34, and the probability of selecting a black marble on the first draw is 0.47. What is the probability of selecting a white marble on the second draw, given that the first marble drawn was black? P (White|Black)  =      P(Black and White)               =  0.34    P(black)                                  0.47                                                = 72% Thanks Blaine!