Question

Help with number four a-d is all of number four

Answer 1

d)

1) Let's begin with that by finding the probability of picking each drink

We need then to find the sample space, the total number of drinks: 14+28+7=49

The probability of picking water is found by:

`P=(14)/(49)=(2)/(7)=0.2857`

The probability of picking cola is then:

`P(cola)=(28)/(49)=(4)/(7)=0.5714`

And the probability of picking Lemonade is:

`P(lemonade)=(7)/(49)=(1)/(7)=0.1428`

2) Now, let's analyze the statements:

a) You are twice as likely to select cola than water:

Let's divide these probabilities and check:

`(P(cola))/(P(water))=((4)/(7))/((2)/(7))=(4)/(7)\cdot(7)/(2)=2`

True

b)

`(P(lemonade))/(P(water))=((1)/(7))/((2)/(7))=(1)/(7)*(7)/(2)=(1)/(2)`

True

c) We can compare the probabilities in their decimal form:

`P(cola)=0.5714,P(water)=0.2857,P(lemonade)=0.1428`

True

d)

`\begin{gathered} P(water)=0.28 \\ P(cola)=0.57 \end{gathered}`

False