Question

An eight-sided die, which may or may not be a fair die, has four colors on it; you have been tossing the die for an hour and have recorded the color rolled for each toss. What is the probability you will roll a yellow on your next toss of the die? Express your answer as a simplified fraction or a decimal rounded to four decimal places.

Answer 1

Answer:

Case 1

None of the sides is yellow.

Probability of rolling a yellow on your next toss: zero %

Case 2

All the sides are yellow.

Probability of rolling a yellow on your next toss: 100 %

Case 3  

At least one of the sides is yellow.

$\frac{q}{N}\times100\%$

where  

N = total number of tosses  in one hour.

q = number of tosses you rolled a yellow.

Step-by-step explanation:

Case 1

None of the sides is yellow.

Probability of rolling a yellow on your next toss: zero %

Case 2

All the sides are yellow.

Probability of rolling a yellow on your next toss: 100 %

Case 3  

At least one of the sides is yellow.

As you do not know if the die is fair or not, the only way to approximate a probability of rolling a yellow is by making a table of frequencies and record the times you have rolled yellow.

If the number of tosses made in an hour is big enough as to draw a conclusion, then according to the Law of Large Numbers, the probability of rolling a yellow in one toss of the die should be

$\frac{q}{N}\times100\%$

where  

N = total number of tosses

q = number of tosses you rolled a yellow.

Now, suppose you want to roll the dice once more.  

As the event of rolling a die is independent of the previous tosses, this means that the probable outcome of the event does not depend on the previous results. So, the probability remains the same.  

Probability of tossing a yellow on your next toss of the die

$\frac{q}{N}\times100\%$

where  

N = total number of previous tosses

q = number of tosses you rolled a yellow.