# Chapter 5

## 5.1

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

## 5.10

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

## 5.15

a)$$1/16$$
b)$$4/16=1/4$$
c)$$6/16=3/8$$
d)$$4/16=1/4$$
e)$$1/16$$

## 5.21

$$104/1858=5.6\%$$

## 5.22

$$26/1858=1.4\%$$

## 5.23

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

## 5.24

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

## 5.25

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

## 5.33

a)$$P(Odd or less than 3)=3/6+2/6-1/6=4/6=66.7\%$$
b)$$P(Odd or less than 2)=3/6+1/6-1/6=50\%$$

## 5.40

a)$$15/50= 30\%$$
b)$$35/50=70\%$$
c)30/50=60%$$\\ d)20/50=40\%$$
e)1 because they are compliments.

## 5.44

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.

## 5.47

a)$$306/530=57.7\%$$
b)$$104/593=17.53\%$$
c)The highest percent is with liberal democrats.

## 5.57

$$P(Right)=60/100=60\%$$
$$18/30=60\%$$
since the two probabilities are equal we can say these are independent.

## 5.59

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.

## 5.61

a) $$(0.5)^3=1/8$$
b) $$0.5*0.5*0.5=1/8$$

## 5.63

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 $$(\frac{1}{6})^5$$

## 5.65

a)Neither fastened is $$1-0.84=0.16$$ then for two people, $$(0.16)(0.16)=0.0256$$
b)$$1-0.0256=0.9744$$

## 5.69

a) HTHTH HHTTT THHTH HHHTT
b) $$11/20$$