Quinta is rolling a dice and keeping track of the number she gets on each roll. The table below summarizes her results.

Question

Rolling a Dice
Number Frequency
1 15
2 17
3 14
4 16
5 15
6 14


What are the experimental and theoretical probabilities of rolling the number 4? Round your answer to the nearest thousandth.

Experimental probability
=


Theoretical probability
=

Answer 1

To find the experimental and theoretical probabilities of rolling the number 4, we will use the frequencies provided in the table.

Experimental Probability:

1. First, we need to find the total number of rolls. We sum the frequencies:

   \[ \text{Total rolls} = 15 + 17 + 14 + 16 + 15 + 14 = 91 \]

2. Next, we identify the frequency of rolling a 4, which is given as 16.

3. The experimental probability \(P(E)\) of rolling a 4 is calculated as:

   \[ P(E) = \frac{\text{frequency of rolling a 4}}{\text{total rolls}} = \frac{16}{91} \]

   Now we calculate \( \frac{16}{91} \):

   \[ P(E) \approx 0.175824 \]

   Rounding to the nearest thousandth, we have:

   \[ P(E) \approx 0.176 \]

Theoretical Probability:

The theoretical probability \(P(T)\) of rolling a 4 on a fair six-sided die is calculated assuming each side has an equal chance of landing face up:

\[ P(T) = \frac{1}{6} \approx 0.1667 \]

Rounding to the nearest thousandth, we have:

\[ P(T) \approx 0.167 \]

Final Answers:

• Experimental probability = 0.176
• Theoretical probability = 0.167