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 times. What proportion of the 10 rolls resulted in a "one"? (b) After 20 rolls of the die, you observe a "one" a total of 5 times. What proportion of the 20 rolls resulted in a "one"? (a) The proportion was $$ \square $$. (Simplify your answer. Do not round.)

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UpStudy AI · Accepted Answer

To find the proportion of rolls that resulted in a "one," we can use the formula:

$$
\text{Proportion} = \frac{\text{Number of "ones"}}{\text{Total rolls}}
$$

### (a) After 10 rolls of the die:
- Number of "ones" = 1
- Total rolls = 10

Using the formula:

$$
\text{Proportion} = \frac{1}{10}
$$

### (b) After 20 rolls of the die:
- Number of "ones" = 5
- Total rolls = 20

Using the formula:

$$
\text{Proportion} = \frac{5}{20}
$$

Now, let's simplify both proportions.

1. For (a):

$$
\frac{1}{10} \text{ is already in simplest form.}
$$

2. For (b):

$$
\frac{5}{20} = \frac{1}{4} \text{ (simplifying by dividing both numerator and denominator by 5).}
$$

### Final Answers:
(a) The proportion was $$ \frac{1}{10} $$.  
(b) The proportion was $$ \frac{1}{4} $$.
(a) The proportion was $$ \frac{1}{10} $$. (b) The proportion was $$ \frac{1}{4} $$.

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