Sadiq rolls a regular six-sided number cube 10 times and gets an even number 7 times. How does his experimental probability compare to the theoretical probability?(1 point) Responses The experimental and theoretical probability are equal. The experimental and theoretical probability are equal. The experimental probability was greater than the theoretical probability. The experimental probability was greater than the theoretical probability. The theoretical and experimental probabilities are opposites. The theoretical and experimental probabilities are opposites. The theoretical probability is greater than the experimental probability.

1 answer

To analyze Sadiq's situation, we first need to determine both the theoretical and experimental probabilities of rolling an even number on a six-sided die.

  1. Theoretical Probability: In a regular six-sided number cube (die), the even numbers are 2, 4, and 6. Thus, there are 3 even outcomes and 3 odd outcomes. The theoretical probability of rolling an even number is:

    \[ P(\text{even}) = \frac{\text{number of even outcomes}}{\text{total outcomes}} = \frac{3}{6} = \frac{1}{2} \]

  2. Experimental Probability: In Sadiq's experiment, he rolled the die 10 times and got an even number 7 times. The experimental probability of rolling an even number is:

    \[ P(\text{even, experimental}) = \frac{\text{number of even outcomes in experiment}}{\text{total rolls}} = \frac{7}{10} = 0.7 \]

Now, we can compare the two probabilities:

  • Theoretical probability: 0.5 (or 50%)
  • Experimental probability: 0.7 (or 70%)

Since 0.7 (the experimental probability) is greater than 0.5 (the theoretical probability), we conclude:

The experimental probability was greater than the theoretical probability.