1.6 Probability 9.7 Probability of Multiple Events 12.2 Conditional Probability.

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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 (0100%)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 sixsided 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 52card 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(nonface 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 #614 (even), 2533
Section 9.7 “multiple event” Probability p. 534 #1,2, 5, 9, 13, 16, 1925 (odd),37,39,45p. 542 #36
Section 12.2 “Conditional” Probabilityp. 136 #113 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)