Chapter 5, Problem 1PE

Lauren drinks a variety of soft drinks. Over the past month, she has had $17$ diet colas, $3$ cans of lemonade, and $5$ cans of root beer in no particular order or pattern.

1. Given this history, what is the probability that her next drink 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 that her next drink will be on diet cola, lemonade, root beer respectively, given the history in question.

Answer to Problem 1PE

  $\begin{array}{l}\text{P(Diet Cola)}=0.68\\ \text{P(Lemonade)}=0.12\\ \text{P(Root Beer)}=0.2\end{array}$

Explanation of Solution

As we know that the probability of the outcome is the probability of the favorable outcomes divided by the probability of the total outcomes.

It is given in the question that,

The number of cans of Diet Colas are $17$ .

The number of cans of Lemonade are $3$ .

The number of Root Beer are $5$ .

Thus, the total number of outcomes are

  $\begin{array}{l}17+3+5\\ =25\end{array}$

Therefore,

P(Diet Colas) $\begin{array}{l}=\frac{17}{25}\\ =0.68\end{array}$

  $\begin{array}{l}\text{P(Lemonade)}=\frac{3}{25}\\ =0.12\end{array}$

  $\begin{array}{l}\text{P(Root Beer)}=\frac{5}{25}\\ =0.2\end{array}$

To determine

To define the definition of probability that we use to answer this question.

Explanation of Solution

The probability used in this question is based on the prior results. Therefore, this is the case of Empirical probability.