Chapter 5, Problem 1PE

Lauren drinks a vanety of soft dnnks. Over the past month, she has had 15 diet colas, 4 cans of lemonade, and 6 cans of root beer in no particular order or pattern.

1. Given this history, what is the probability that her next dnnk will be a diet cola? Lemonade? Root beer?
2. What definition of probability did you use to answer this question?

To determine

To find: The probability of next drink will be $\left(\text{i}\right)$ A diet cola, $\left(\text{ii}\right)$ A lemonade,and $\left(\text{iii}\right)$ A root beer.

Answer to Problem 1PE

  $\begin{array}{l}P(\text{Drink a diet cola})=0.6\\ P(\text{Drink a lemonade})=0.16\\ P(\text{Drink a root beer})=0.24\end{array}$

Explanation of Solution

Given information:

The below table represents the number of soft drinks that Lauren has drink over the past month.

  $\boxed{\begin{array}{cc}SoftDrink& Number\\ \text{Diet cola }& 15\\ \text{Lemonade }& 4\\ \text{Root beer }& 6\end{array}}$

Calculation:

In this question, there are no patterns or orders to drink. Therefore the following formula can be used to calculate the probabilities:

  $\text{Probaility of an event A =}\frac{\text{Number of times that A has occurred}}{\text{Total number of outcomes}}$

The total number of soft drinks is

  $15+4+6=25$ .

  $\begin{array}{l}P(\text{Drink a diet cola})=\frac{15}{25}=0.6\\ P(\text{Drink a lemonade})=\frac{4}{25}=0.16\\ P(\text{Drink a root beer})=\frac{6}{25}=0.24\end{array}$

To determine

To state: The definition that used to find the probability in part (a).

Answer to Problem 1PE

The probability of an event is equal to the relative frequency of the outcomes of that event.

Explanation of Solution

Thereare no patterns or orders to drinkin this question. The following formula is used to calculate the probabilities:

  $\text{Probaility of an event A =}\frac{\text{Number of times that A has occurred}}{\text{Total number of outcomes}}$

Therefore the definition that used to find the probability is:

The probability of an event is equal to the relative frequency of the outcomes of that event.

It is called as Relative Frequency Definition of Probability.