a)2,6,4,2,7,4,0,6,5,0

b)T,T,T,T,H, T,T,T,H,T

c)No I only got 2 heads

\(7/4, -10\%\) cant be real probabilities for \(7/4\) is larger than one and we cant have negative probabilities.

a)\(1/16\)

b)\(4/16=1/4\)

c)\(6/16=3/8\)

d)\(4/16=1/4\)

e)\(1/16\)

\(104/1858=5.6\%\)

\(26/1858=1.4\%\)

Were looking at the total numbers for Democrat or Republican, and since this is an or questions we add \((689+469)/1858=62.3\%\)

\((593+530/1858=60.4\%\)

Following the guided excersice\(P(Liberal)=530/1858=28.5\%\)

\(P(Democrat)=689/1858=37.1\%\)

They arent mutually exclusive because you can see that there are people who are both liberal and democrat.

\(P(Lib and Dem)=(306)/1858=16.5\%\)

If we dont subtract away the probability of people being democrat and liberal from that equation, you will be over counting.

\(P(Lib or Dem)=(530+689-306)/1858=49.1\%\)

a)\(P(Odd or less than 3)=3/6+2/6-1/6=4/6=66.7\%\)

b)\(P(Odd or less than 2)=3/6+1/6-1/6=50\%\)

a)\(15/50= 30\%\)

b)\(35/50=70\%\)

c)30/50=60%\(\\
d)20/50=40\%\)

e)1 because they are compliments.

a)\(1-0.23-0.41=0.36\)

b)\(0.41+0.36=0.77\)

c)\(0.41+0.23=0.64\)

d)a and c are complementary.16 or more mistakes mean 16 up to 30. 15 or fewer all values from 0 up to 15. If you add these together you get the whole experiment.

a)\(306/530=57.7\%\)

b)\(104/593=17.53\%\)

c)The highest percent is with liberal democrats.

Follow the guided exercise

\(P(Right)=60/100=60\%\)

\(18/30=60\%\)

since the two probabilities are equal we can say these are independent.

a)

b) \(P(happy|agree)=345/379=91\%\)

\( P(happy)=1262/1362=92.7\%\)

The percentages are close together, but independence needs that these percentages need to be equal.So they are not independent.

a) \((0.5)^3=1/8\)

b) \(0.5*0.5*0.5=1/8\)

They are both the same probability.Each time you flip a coin there is a probability of \(1/6\) to roll any number from 1-6, so total probability here \((\frac{1}{6})^5\)

a)Neither fastened is \(1-0.84=0.16\) then for two people, \((0.16)(0.16)=0.0256\)

b)\(1-0.0256=0.9744\)

a) HTHTH HHTTT THHTH HHHTT

b) \(11/20\)