Questions: Salma rolled a number cube 150 times and got the following results. Outcome Rolled: 1, 2, 3, 4, 5, 6 Number of Rolls: 28, 25, 17, 19, 35, 26 Answer the following. Round your answers to the nearest thousandths. (a) From Salma's results, compute the experimental probability of rolling a 6. (b) Assuming that the cube is fair, compute the theoretical probability of rolling a 6.

Solution Steps

To solve the given problem, we need to compute both the experimental and theoretical probabilities of rolling a 6 on a number cube.

(a) Experimental Probability: This is calculated by dividing the number of times a 6 was rolled by the total number of rolls.

(b) Theoretical Probability: For a fair number cube, each outcome (1 through 6) is equally likely. Therefore, the theoretical probability of rolling a 6 is 1 out of 6.

The experimental probability of rolling a 6 is calculated by dividing the number of times a 6 was rolled by the total number of rolls. Given:

• Total rolls: \( 150 \)
• Rolls of 6: \( 26 \)

The experimental probability \( P_{\text{exp}}(6) \) is: \[ P_{\text{exp}}(6) = \frac{26}{150} \approx 0.1733 \]

For a fair number cube, each outcome (1 through 6) is equally likely. Therefore, the theoretical probability \( P_{\text{theo}}(6) \) of rolling a 6 is: \[ P_{\text{theo}}(6) = \frac{1}{6} \approx 0.1667 \]

Final Answer