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1.6 Probabili ty9.7 Probabili ty of Multiple Events 12.2 Condition al Probabili

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### Transcript of 1.6 Probability 9.7 Probability of Multiple Events 12.2 Conditional Probability.

1.6 Probabilit

y9.7 Probabilit

y of Multiple Events12.2

Conditional

Probability

Probability

Measures how likely it is that an event will occur.Expressed as

A Percentage (0-100%)or

a number between 0 and 1

Experimental Probability

Experimental Probability: Based on observation

experimentin trialsofnumber

occursevent favorable the timesofnumber P

Ex1)

A quarterback throws 40 passes during a game and completes 30 of them. Find the experimental probability of him completing a pass.

passes totalof #passes complete of #P

4030 %75or

43

Theoretical Probability

(Theoretical) Probability: Based on what would happen in theory.

outcomes possible ofnumber events favorable ofnumber P

Ex2)

Find the probability of rolling a prime number when you roll a regular six-sided die.

iespossibilit of #

numbers prime of #P

63 %50or

21

Example from Venn diagramEx 3) What is the probability of drawing a heart that is not a face card from a deck of 52 cards.

HeartsFace Cards

Everything else

9.7 Probability of Multiple Events

Compound Events

Independent Events(One event does

not affect another event)

Dependent Events(One event affects

another event)

AND

Probability that both Independent Events will occur:

BPAPBAP and

1 2

33

Ex 4) What is the probability of spinning a 3 on the spinner and rolling a 3 on the die?

Ex 5) A card is drawn from a standard 52-card deck. Then a die is rolled. Find the probability of each compound event.

a) P(draw heart and roll 6)

b) P(draw 7 and roll even

c) P ( draw face card and roll < 6)

Compound Events

Compound Events

Ex 6) There are five discs in a CD player. The player has a “random” button that selects songs at random and does not repeat until all songs are played. What is the probability that the first song is selected from disc 3 and the second song is selected from disc 5?

Disc 2 10 songs

Disc 4 9 songs

Disc 3 13 songs

Disc 1 8 songs

Disc 5 10 songs

Why are these independent events?

Ex 7) A drawer contains 4 green socks and 5 blue socks. One sock is drawn at random. Then another sock is drawn at random.

a. Suppose the first sock is returned to the drawer before the second is drawn at random. Find the probability that both are blue.

b. Suppose the first sock is not returned to the drawer before the second is drawn. Find the probability that both are blue.

If A and B are mutually exclusive events, then

If A and B are not mutually exclusive events, then

Probability with “OR”

BPAPBAP or

BAPBPAPBAP and or

What is the probability event A or event B could occur?

Mutually Exclusive Events: two events that CANNOT happen at the same time

Subtract the overlap

OR

Example 8)a. P(face card) =

b. P(non-face card) =

c. P(face card or ace) =

d. P(two or card < 6) =

e. P(not a jack) =

f. P(red card or seven) =

g. P(ace or king) =

HW Assignment

Section 6.7 “Basic” Probabilityp. 42 #6-14 (even), 25-33

Section 9.7 “multiple event” Probability p. 534 #1,2, 5, 9, 13, 16, 19-25 (odd),37,39,45p. 542 #36

Section 12.2 “Conditional” Probabilityp. 136 #1-13 all

Example 9)Yes, Did a chore last night

No, Did NOT do a chore

Male 2 7

Female 6 3

femaleP

nightlast chore a did AND femaleP

nightlast chore a didP

Section 12.2: Conditional Probability

Conditional Probability Formula:“Probability of event B, given that event A has occurred”

ABP |“given”

nightlast chore a did | femalePEx 10)

Yes, Did a chore last night

No, Did NOT do a chore

Male 2 7

Female 6 3

AP

BAP and

Conditional ProbabilityEx 11) A cafeteria offers vanilla and chocolate ice cream, with or without fudge sauce. The manager kept records on the last 200 customers who ordered ice cream.

Fudge Sauce No Fudge Sauce Total

Vanilla Ice Cream 64 68 132

Chocolate Ice Cream 41 27 68

Total 105 95 200

a. P(includes fudge sauce)

b. P(includes fudge sauce | chocolate ice cream)

c. P(chocolate ice cream | includes fudge sauce)

Fudge Sauce No Fudge Sauce Total

Vanilla Ice Cream 64 68 132

Chocolate Ice Cream 41 27 68

Total 105 95 200

Conditional Probability

d. P(vanilla ice cream with no fudge sauce)

e. P(vanilla ice cream | does not include fudge sauce)

f. Find the probability that the order has no fudge sauce, given that it has vanilla ice cream.

Tree Diagrams – Ex 12)