Tree Diagrams
Draw a tree diagram for the following probability. I have 2 draws from a bag of marbles without replacement. The bag contains 4 white marbles and 7 Green marbles.
will draw diagram on the board
Calculate the correlation coefficient and make a conclusion about the type of correlation for the data: x= 8, 7, 7, 8, 6, 5, 7, 4, 9, 7 y=83, 86, 78, 88, 76, 66, 90, 60, 89, 81
r=0.90346 so strong linear correlation
Draw a Venn Diagram and shade the region for P(A'UB)
shade everything except the just A section
Who was the first American President?
George Washington
Given the data: 0, 1, 1, 2, 2, 2, 3, 4, 5, 6 find the Mean, Variance, and Standard Deviation.
Mean= 2.6 Variance=3.24 Standard deviation=1.8
A bag contains 4 red and 6 blue marbles. You draw two marbles without replacement. What is the probability that you draw two different colors?
P(2 different colors)=8/15
find the correlation coefficient and make a conclusion about the type of correlation for the data:
x= 0, 1, 2, 3, 3, 5, 5, 5, 6, 7, 7, 10
y=96, 85, 82, 74, 95, 68, 76, 84, 58, 65, 75, 50
r=-.8313 so strong negative correlation
Given that P(A)=.5 P(B)=.45 and P(A^B)=.3 find P(AUB')
P(AUB')=.2+.3+.35=.85
Where would one arrive at the second star to the right, and straight on till morning?
Neverland
Sketch a Box-and-Whisker plot for the data. 46, 48, 48, 50, 52, 47, 51, 47, 49, 53
Will draw picture on board but min=46, Q1=47, Med=48.5, Q3=51 max=53
The probability that Bob remembers to set his alarm is 2/5. if he sets his alarm the probability he is on time is 2/3. If he doesn't set his alarm the probability he is on time is 1/10. Create a tree diagram. Given that Danny was not late what is the probability that he remembered to set his alarm?
P(SlL')=P(S^L')/P(L')=(4/15)/((4/15)+(3/50))=(4/15)/(49/150)=40/49
Find the LSRL for the data:
X= 186, 181, 176, 149, 184, 190, 158, 139, 175, 148
Y= 495, 477, 425, 322, 482, 587, 370, 322, 479, 375
y=-299.48+4.35x
Given mutually exclusive events A and B where P(A)=.75 and P(B)=.25 find P(A^B)
P(A^B)=0 explain why?
Which country gave the USA the ‘Statute of Liberty?
France
Sketch a Box-and-Whisker plot for the data 19, 12, 14, 9, 15, 16, 18, 13, 19, 10, 11, 19
min=9 Q1=11.5 med=14.5 Q3=18.5 max=19
If you take two draws from a bag containing 4 red, 2 blue, and 3 green marbles. Draw a tree diagram. What is the probability of getting two marbles of a different color?
1-(RR+BB+GG) = 1-5/18=13/18 or RG+RB+BR+BG+GB+GR=1/9+1/6+1/9+1/12+1/6+1/12 = 13/18
Calculate the LSRL and then solve the predictions using the given data.
X=17, 23, 27, 32, 35
y=132, 153, 170, 173, 186
Predict the Y value for when X= 18, 27, 32, and 40
LSRL Y=86.4043+2.8506x
When X=18 Y=137.72
X=27 Y=163.37
X=32 Y=177.62
X=40 Y=not possible
Given two independent events A and B where P(A)=.3 and P(B)=.2 find P(AlB')
P(AlB')=3/10 or .3
What is the most popular board game of all time?
Chess
Find the Mean, Variance, Standard Deviation, and identify any outliers if there are any for the given data: 99, 125, 120. 150, 210, 198, 194, 183, 168, 153, 143, 120, 117, 165
mean=153.21 Variance=1107.6 Standard Deviation=33.28 Outliers: no outliers
The events B and C are dependent, where C is the event a student takes calculus and B is the even a student studies Bioengineering in college. Given: P(C)=.4 P(BlC)=.6 P(BlC')=.5 Create a tree diagram. Given a student studies Bioengineering what is the probability that the student takes Calculus?
P(ClB) = P(C^B)/P(B) = .24/(.30+.24) = .24/.54 = 24/54 = 4/9 or .44444444444
Find the LSRL, correlation coefficient, make a conclusion about the type of correlation, and solve the predictions.
Data:
Years of experience: 1, 3, 5, 6, 8, 10, 14
Hourly Pay: 6, 8.27, 10.43, 12, 14, 18, 23
predict for 2, 4, 7, 9, and 16 years of experience
LSRL Y=4.3205+1.321x, r=.997, strong positive linear correlation, 2 years experience $6.96, 4 years experience $9.60, 7 years experience $13.57, 9 years experience $16.21, 16 years of experience not possible to find
Given that P(A)=.5, P(B)=.3, P(AUB)=.6 find P(AlB)
first find the intersection .6=.5+.3-P(A^B) solve that get .2 for P(A^B) then solve P(AlB) get .2/.3 =2/3 or .66666666
In 1952, Albert Einstein was offered the presidency of which country?
Israel
Find the Mean, Variance, Standard Deviation, and identify any outliers if there are any for the given data: 97, 98, 110, 129, 128, 123, 128, 139, 136, 134, 132, 136, 140, 127, 122, 121, 158
Mean=126.94 Variance=213.11 Standard Deviation= 14.598 Outliers: 97, 98, 158