5.2B Multiplication Rules
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Transcript of 5.2B Multiplication Rules
5.2B Multiplication Rules
Independent EventsDependent Events
General Multiplication Rule
Independent and Dependent Events
Independent Events: Two events are independent if
knowing that one will occur (or has occurred)
does not change the probability that the
otheroccurs.
Independent and Dependent Events
Dependent Events: Two events are dependent if knowing
that one will occur (or has occurred)
changes the probability that the other occurs.
Example #1
The following are examples of independent
events:a. Rolling a die AND getting a 6, and
then rolling a second die and getting a 3.
b. Drawing a card from a deck AND getting a queen, replacing it, then drawing a second card and
getting a king.
Example #1
The following are examples of independent
events:c. Being on time to school AND your
teacher being on time to school.d. Choosing a marble from a jar
AND tossing a coin that lands on heads.
Example #2
The following are examples of dependent
events:a. The speed you drive to school
AND the weather.b. Choosing a marble from a jar,
not replacing it, AND drawing another marble from that same jar..
Example #2
The following are examples of dependent
events:c. Eating a full breakfast AND
being on time to school.d. Parking in a no-parking zone
AND getting a parking ticket.
Determine whether the events are independent or dependent.a.Tossing a coin and drawing a marble
out of a bag.INDEPENDENT
b.Eating sweets and having diabetes.DEPENDENT
Example #3
Example #3
Determine if the events are independent or
dependent.c.Being on the Indianapolis Colts football
team and being a winnerDEPENDENT
d.Drawing a king from a standard deck, replacing it and drawing another king.INDEPENDENT
Multiplication Rule For Independent Events
If events A and B are independent,
BPAPBandAP
Example #4
A dresser drawer contains one pair of socks of each of the following colors: blue, brown, red, white and black. Each pair is folded together in matching pairs. You reach into the sock drawer and choose a pair of socks without looking. The first pair you pull out is red -the wrong color.
You replace this pair and choose another pair. What
is the probability that you will choose the red pair of socks twice?
Example #4
Indepdendent?Yes
)( RandRP )()( RPRP
04.5
1
5
1
Example #5
A coin is tossed and a single 6-sided die is
rolled. Find the probability of landing on the head side of the coin and rolling a 3
on the die. Independent?Yes
Example #5
33 PHPandHP
083.12
1
6
1
2
1
Example #6
A card is chosen at random from a deck of
52 cards. It is then replaced and a second
card is chosen. What is the probability of choosing a face card and an eight? Independent?Yes
Example #6
88 PFacePandFaceP
018.52
4
52
12
Example #7
A South Carolina survey of registered voters
found that 65% were opposed to the new Health Care Plan. Suppose you randomly choose 5 South Carolinians. What is the probability all 5 of them oppose the health care plan?Independent?Yes
Example #7
OandOandOPopposeP 3
275.65.65.65.65. 3
General Multiplication Rule
Given events A and B, the probability of
both A and B occurring is:P(A and B) = P(A)P(B|A), Where P(B|A) is the probability that B
occurs given A has occurred.
Example #8
A card is chosen at random from a standard deck of 52 playing cards. Without replacing it, a second card is chosen. What is the probability that the first card chosen is a queen and the second card chosen is a jack? Independent?No
Example #8
QJPQPJandQP |
00603.51
4
52
4
Example #9
Mr. Parietti needs two students to help him with a science demonstration for his class of 18 girls and 12 boys. He randomly chooses one student who comes to the front of the room. He then chooses a second student from those still seated. What is the probability that both students chosen are girls? Independent?No
Example #9
GGPGPGP |2
152.29
11
30
12
Example #10
In a shipment of 20 computers, 3 are defective. Three computers are randomly selected and tested. What is the probability that all three are defective if the first and second ones are not replaced after being tested? Independent?No
Example #10
DDPDDPDPDefectiveP 2|1|3
00088.18
1
19
2
20
3
Example #11
On a math test, 5 out of 20 students got an A. If three students are chosen at random without replacement, what is the probability that all three got an A on thetest? Independent?No
Example #11
sAAPAAPAPsAP '2|1|'3
0088.18
3
19
4
20
5
Example #12
A jar contains 6 red balls, 3 green balls, 5 white balls and 7 yellow balls. Two balls are chosen from the jar, with replacement. What is the probability that both balls chosen are green? Independent?Yes
Example #12
GPGPGP 2
0204.21
3
21
3
Example #13
A nationwide survey showed that 73% of all children in the United States dislike eating vegetables. If 5 children are chosen at random, what is the probability that all 5 dislike eating vegetables?Independent?Yes
Example #13
55 VeggiesDislikePVeggiesDislikeP
207.73. 5
Example #14
A school survey found that 7 out of 30 students walk to school. If four students are selected at random without replacement, what is the probability that the first two chosen walk to school and the next two do not walk to school? Independent?No
Example #14
)12|(2||
'2,2
DWWandDWPWDWPWWPWP
WalktDonWalkP
056.17
12
18
13
19
6
20
7