1. to Calculate a Probability When Outcomes Are Equally Likely, We Can Use the Formula

PROBABILITY

1. To calculate a probability when outcomes are equally likely, we can use the formula:

n(E) P(E)  , where E is an event in a sample S with equally likely outcomes. n(S)

What is the probability that a total of four shows when we roll two fair dice?

The sample space for rolling two dice has 36 ordered pairs of numbers. We will represent the event “rolling a four” by F. Then F = {(1,3), (2,2), (3,1)}.

Therefore,

n(F) 3 1 P(F)    n(S) 36 12

Sample Space (S)

2. To calculate the probability of the complement E’ has probability 1-P(E) of an event we can use the formula:

P(E)  1 P(E) E has probability If the probability of E is .25, we can find the P(E) probability of the complement of E by:

P(E’) = 1-.25 = .75

3. To find the probability of a union of two events, we can use the formula:

P(E  F)  P(E)  P(F)  P(E  F)

What is the probability that we draw either a heart or a face card from a standard 52 card deck?

13 12 3 22 11 P(H  F)  P(H )  P(F)  P(H  F)      52 52 52 52 26

We add the probability of a heart with the probability of a face card, and then subtract the probability of a heart that is a face card to find our answer.

The Academic Support Center at Daytona State College (Math 65 pg 1 of 2) 4. When we compute the probability of an event F assuming an event E has already occurred, this is called the conditional probability of F, given E. To find the conditional probability we can use the formula:

P(E  F) n(E  F) P(F | E)   P(E) n(E) All Face Cards F  Q Queen Total

We draw 1 face card from a 52 card deck, what is the probability that it is a queen? JH, KH, QH, JS, KS, QS, P(F  Q) n(F  Q) 4 1 JC, KC, QC, P(Q | F)     JD KD QD P(F) n(F) 12 3

To compute this, we take the probability of drawing a face card AND a queen, P(F  Q) , and divide it by the probability of drawing any face card P(F).

The Academic Support Center at Daytona State College (Math 65 pg 2 of 2)