THE MATHEMATICAL STUDY OF RANDOMNESS

SAMPLE SPACE the collection of all possible outcomes of a chance experiment

Roll a die S={1,2,3,4,5,6}

EVENT any collection of outcomes from the sample space

Rolling a prime # E= {2,3,5}

COMPLEMENT Consists of all outcomes that are not in the event

Not rolling a even #EC={1,3,5}

UNION the event A or B happening

consists of all outcomes that are in at least one of the two events

Rolling a prime # or even numberE={2,3,4,5,6}

BAE

INTERSECTION the event A and B happening

consists of all outcomes that are in both events

Drawing a red card and a “2” E = {2 hearts, 2 diamonds}

BAE

MUTUALLY EXCLUSIVE

(DISJOINT)two events have no outcomes in common

Roll a “2” or a “5”

VENN DIAGRAMSUsed to display relationships between events

Helpful in calculating probabilities

VENN DIAGRAM - COMPLEMENT OF A

AA

VENN DIAGRAM - A OR B

A B

VENN DIAGRAM - A AND B

A B

VENN DIAGRAM - DISJOINT EVENTS

A B

Com Sci

Statistics & Computer Science & not Calculus

Stat Cal

Com Sci

Calculus or Computer Science

Stat Cal

Com Sci

(Statistics or Computer Science) and not Calculus

Stat Cal

Com Sci

Statistics and not (Computer Science or Calculus)

Stat Cal

Com Sci

Stat Cal

Com Sci

Statistics or Computer Science?

30 10520

1010

20

80

170

Stat Cal

Com Sci

Statistics and Computer Science?

30 10520

1010

20

80

20

Stat Cal

Com Sci

Statistics or (Computer Science and Calculus)?

30 20 105

10 20

80

10

90

Stat Cal

Com Sci

(Statistics or Computer Science) and Calculus?

30 20 105

1010

20

80

50