Chapter 13.4, Problem 1CYU

To determine

To calculate:

The probability of biology quiz using the geometric models.

Answer to Problem 1CYU

The probability that the Clara gets an $A$ on the next quiz is $80\%$ , and the probability of getting a non- $A$ grade is $20\%$ .

Explanation of Solution

Given information:

Clara’s percentgae $=80\%$

Calculation:

Suppose, a student gets an $A$ on a certain subject quiz $80\%$ of the time in the first semester of the class.

Based on geometric model, let the rolls of a six-sided die simulate the students grades on quizzes for the second semester of the class.

So, during the first semester the student got $A\text{'}s$ in the quizzes $80\%$ of the time, so let the numbers $1-4$ on the die represent an $A$ , and let the number $5$ represent a grade other than $A$ and roll again when the number $6$ comes up.

Now roll a die $20$ times, the frequency of outcomes will vary between set of $20$ rolls. One such set of rolls can be recorded table as follows:

Outcome	Frequency
$A$	$16$
$Non-A$	$4$
$Total$	$20$

Now, divide each frequency in the frequency table to get the probabilities for each outcome.

Outcome	Frequency	Probability
$A$	$16$	$\frac{16}{20}=0.80$
$Non-A$	$4$	$\frac{4}{20}=0.20$
$Total$	$20$	$\frac{20}{20}=1$

Make a probability histogram by charting probability on the vertical axis and outcomes on the horizontal axis.

  

Hence, therefore the probability that the student gets an $A$ on the next quiz is $80\%$ , and the probability of getting a non- $A$ grade is $20\%$ .