Question

Suppose you physically simulate the random process of rolling a single die. ​(a) After 1010 rolls of the​ die, you observe a​ "one" 44 times. What proportion of the rolls resulted in a​ "one"? ​(b) After 2020 rolls of the​ die, you observe a​ "one" 22 times. What proportion of the rolls resulted in a​ "one"?

Answer 1

A) 40%

B) 10%

Explanation:

A) p = 4/10 = 40%

B) p = 2/20 = 10%

Answer 2

(a) 4.356% (b) 1.089%

Explanation:

The rolling of a single die is an example of a discrete uniform distribution, where each of the six possible outcomes has an equal probability of 1/6.

(a) After 1010 rolls of the die, observing a "one" 44 times, the proportion of rolls resulting in a "one" is:

Proportion = Number of "ones" / Total number of rolls

= 44 / 1010

= 0.04356

Therefore, approximately 4.356% of the rolls resulted in a "one".

(b) After 2020 rolls of the die, observing a "one" 22 times, the proportion of rolls resulting in a "one" is:

Proportion = Number of "ones" / Total number of rolls

= 22 / 2020

= 0.01089

Therefore, approximately 1.089% of the rolls resulted in a "one".