Suppose you physically simulate the random process of rolling a single die.
(a) After 10 rolls of the die, you observe a "one" a total of 1 time. What proportion of the 10 rolls resulted in a "one"?
(b) After 20 rolls of the die, you observe a "one" a total of 4 times. What proportion of the 20 rolls resulted in a "one"?
(a) The proportion was
(Simplify your answer. Do not round.)
(b) The proportion was
(Simplify your answer. Do not round.)
Answer (2)
The proportion of rolls that resulted in a "one" after 10 rolls is 10 1 , and after 20 rolls, it is 5 1 .
;
Calculate the proportion of rolls resulting in a "one" for 10 rolls: 10 1 .
Calculate the proportion of rolls resulting in a "one" for 20 rolls: 20 4 .
Simplify the fraction 20 4 to 5 1 .
The proportions are 10 1 and 5 1 .
Explanation
Understand the problem In this problem, we are asked to find the proportion of rolls that resulted in a "one" in two separate scenarios. The proportion is calculated by dividing the number of times a "one" was observed by the total number of rolls.
Calculate the proportion for (a) (a) In the first scenario, the die was rolled 10 times, and a "one" was observed 1 time. Therefore, the proportion of rolls that resulted in a "one" is: 10 1 This fraction is already in its simplest form.
Calculate the proportion for (b) (b) In the second scenario, the die was rolled 20 times, and a "one" was observed 4 times. Therefore, the proportion of rolls that resulted in a "one" is: 20 4 We can simplify this fraction by dividing both the numerator and the denominator by their greatest common divisor, which is 4: 20 ÷ 4 4 ÷ 4 = 5 1
State the final answer Therefore, the proportion of rolls that resulted in a "one" in the first scenario is 10 1 , and in the second scenario, it is 5 1 .
Examples
Understanding proportions is useful in many real-life situations. For example, if you're analyzing customer feedback, you might want to know the proportion of customers who are satisfied with your product. If you survey 100 customers and 80 of them are satisfied, the proportion of satisfied customers is 100 80 = 5 4 = 80% . This helps you understand the overall sentiment towards your product.
