Basic Rules of Probability

Objectives

• Determine if events are mutually exclusive.

• Use probability rules to determine the probability of an event.

• Use a Venn diagram to determine probability of an event.

Vocabulary

• mutually exclusive - events that cannot occur at the same time

Determine if the following events mutually exclusive.

• E is the event of “being a doctor” and F is the event of “being a women”

• E is the event of “being single” and F is the event of “being married”

• E is the event of “being a plumber” and F is the event of “being a stamp collector”

Probability Rules

0)( p

1)(0 Ep

1)( Sp

Probability Rules

)()()()( FEpFpEpFEp

0)( FEp

1)()( EpEp

if E and F are mutually exclusive

Standard Deck of Cards

Find the probability of each of the following:

• a jack and a heart

• a jack or a heart

• not a jack of hearts

• above a jack

• below a three

Find the probability of each of the following:

• both above a jack and below a three

• either above a jack or below a three

• not a jack of hearts

• above a five

• below a jack

If o(E) = 1:6, then find .

Rolling a Pair of Dice

Find the probability that the sum when a pair of dice is rolled is

• 8 or 10

• even and less than 5

• even or less than 5

Alex is taking two courses, algebra and U. S. history.  Student records indicate that the probability of passing algebra is .35, that of failing U. S. history is .35, and that of passing at least one of the two courses is .80.  Find the probability that

• Alex will pass history

• Alex will pass both courses

Alex is taking two courses, algebra and U. S. history.  Student records indicate that the probability of passing algebra is .35, that of failing U. S. history is .35, and that of passing at least one of the two courses is .80.  Find the probability that

• Alex will fail both courses

• Alex will pass exactly one course