Lesson 10-4: Compare Probabilities of Simple Events — Practice Questions

1. 1. The theoretical probability of a spinner landing on blue is $0.25$. Which experiment's result is best explained by the Law of Large Numbers?

   • A. Spinning 10 times gives an experimental probability of $0.3$.
   • B. Spinning 100 times gives an experimental probability of $0.8$.
   • C. Spinning 5,000 times gives an experimental probability of $0.251$.
   • D. Spinning 5 times gives an experimental probability of $0$.

2. 2. A standard six-sided die is rolled. The theoretical probability of rolling a 3 is $\frac{1}{6}$. According to the Law of Large Numbers, after many thousands of rolls, the experimental probability will approach ___.

3. 3. A coin is flipped 20 times, and the experimental probability of getting heads is $0.4$. If the coin is fair, what is expected to happen as the number of flips increases to 10,000?

   • A. The experimental probability will stay at $0.4$.
   • B. The experimental probability will approach $0.5$.
   • C. The experimental probability will approach $1.0$.
   • D. The experimental probability will approach $0$.

4. 4. A bag contains colored marbles. The theoretical probability of drawing a red marble is $0.2$. If you draw a marble 8,000 times (replacing it each time), the number of red marbles drawn would be expected to be close to ___.

5. 5. Alex rolls a die 50 times and Beth rolls the same die 500 times. Whose experimental probability of rolling a '6' is more likely to be closer to the theoretical probability of $\frac{1}{6}$?

   • A. Alex
   • B. Beth
   • C. They are equally likely
   • D. It is impossible to determine

6. 6. A spinner is divided into 8 equal sections. What is the theoretical probability of landing on any single section? Express your answer as a fraction. ___

7. 7. A standard six-sided die is rolled 30 times, and the number '4' appears 6 times. Based on this experiment, what is the probability of rolling a '4'? Express as a simplified fraction. ___

8. 8. A bag contains 5 red and 5 blue marbles. After drawing a marble and replacing it 40 times, you draw a red marble 18 times. How does the experimental probability compare to the theoretical?

   • A. The experimental probability is greater.
   • B. The experimental probability is less.
   • C. The probabilities are equal.
   • D. There is not enough information.

9. 9. A bag contains 5 green, 3 yellow, and 2 blue marbles. What is the theoretical probability of drawing a yellow marble? Express your answer as a fraction. ___

10. 10. In a survey of 80 students, 20 chose pizza as their favorite lunch. Based on this data, what is the experimental probability that a student's favorite lunch is pizza? Express as a simplified fraction. ___