Question

darnell's grandparents sent him a magic kit for his birthday. it includes six-sided weighted dice. he rolls one of the dice repeatedly and records the results. the table below shows the outcomes he records.numbertimes rolled122338435167based on the data, what is the probability that darnell will roll a 3?

Answer 1

The probability that Darnell will roll a 3 is 0.3167, calculated by dividing the number of times a 3 was rolled (38) by the total number of rolls (120) and rounding to four decimal places.

Step-by-step explanation:

To calculate the probability that Darnell will roll a 3, we use the data on the number of times each outcome was rolled. We need to divide the number of times a 3 was rolled by the total number of rolls. Based on the given table:

• Number 3 was rolled 38 times.
• The total number of rolls was 120 times.

The probability P(rolling a 3) is calculated as:

P(rolling a 3) = Number of 3s rolled / Total number of rolls

So, P(rolling a 3) = 38 / 120

We can reduce this fraction to its simplest form, or convert it into a decimal for ease of understanding.

P(rolling a 3) = 0.3167 (rounded to four decimal places)

This probability can be used to predict the likelihood of this event in the future, considering the data that Darnell has recorded.

Answer 2

Based on the data Darnell recorded, the probability of rolling a 3 is 1/3.

To find the probability of rolling a 3 based on Darnell's recorded outcomes, we'll need to use the basic probability formula:

Probability of an event = (Number of times the event occurs) / (Total number of outcomes)

From the table Darnell provided, we see that:

- The number 3 was rolled 8 times.
- The total number of rolls can be calculated by adding up all the times each number was rolled.

Adding up the times each number was rolled:

1 was rolled 2 times
2 was rolled 3 times
3 was rolled 8 times
4 was rolled 3 times
5 was rolled 1 time
6 was rolled 7 times

So the total number of rolls is 2 + 3 + 8 + 3 + 1 + 7 = 24.

Now, we know the number of times 3 was rolled and the total number of rolls, so we can calculate the probability:

Probability of rolling a 3 = (Number of times 3 was rolled) / (Total number of rolls)
Probability of rolling a 3 = 8 / 24

To simplify this fraction, we can divide both the numerator and the denominator by the greatest common divisor, which is 8 in this case:

Probability of rolling a 3 = 1 / 3