Probability

How likely it is that something will happen.

p: symbol to represent the probability of a particular outcome.

# of ways an event can occur

p =

total # of events

The event: rolling a 3 with one die

1 (# of ways the event occurs)

p =

6 ( total # of possible events)

Event: rolling a 5 with a pair of dice

# of ways the event can occur: 4

1 4

2 3

3 2

4 1

Total # of events : 36

1 1 2 1 3 1 4 1 5 1 6 1

1 2 2 2 3 2 4 2 5 2 6 2

1 3 2 3 3 3 4 3 5 3 6 3

1 4 2 4 3 4 4 4 5 4 6 4

1 5 2 5 3 5 4 5 5 5 6 5

1 6 2 6 3 6 4 6 5 6 6 6

Probability of rolling 5 with a pair of dice

4 (# of ways the event can occur)

p =

36 (total number of events)

1

p= p = .11

9

All events: 50 pieces of paper

10 green

20 red

15 yellow

5 blue

(papers are returned after each draw)

1) Prob. of two events both occurring

Event A and Event B

( Prob. A) (Prob. B)

Event: drawing a red and a yellow

All events: 50 pieces of paper

10 green

20 red

15 yellow

5 blue

(papers are returned after each draw)

Event: drawing a red and a yellow

prob of red and prob of yellow

20 15

50 50

20 15 300 3

50 50 2500 25

or:

2 3 6 3

5 10 50 25

p = .12

Probability does not have memory !

If the event is defined as two draws then this method applies.

If the event is limited to the second draw only, the probability is based on that event alone

2) The probability of either of two mutually exclusive events occurring is the sum of their probabilities.

Prob A or Prob B

(Prob A ) + (Prob B)

Event: in one draw, choosing a yellow or red.

All events: 50 pieces of paper

10 green

20 red

15 yellow

5 blue

(papers are returned after each draw)

Event: in one draw, choosing a yellow or red.

20 15 35 7

50 50 50 10

p = .7

Mutually Exclusive:

When two events can not co-occur.

Events that are not mutually exclusive:

Using a standard deck of 52 playing cards,

Drawing a face card or a heart.

12 faces cards

13 hearts

3 cards that are face cards and hearts

Prob A + Prob B - (Prob AB)

12 13 3

52 52 52