Theoretical and Experimental Probability：練習問題

A bag contains 5 red marbles, 3 blue marbles, and 2 green marbles. If a marble is drawn at random, what is the probability that it is not blue?

A weather station records the rainfall for 50 days during the summer. It rained on 15 of those days. If the same conditions persist, what is the experimental probability that it will not rain on a given day during the rest of the summer?

A spinner is divided into 8 equal sectors numbered 1 to 8. If the spinner is spun once, what is the probability that the pointer lands on a number that is a multiple of 3?

In a quality control test, 200 light bulbs were tested and 8 of them were found to be defective. Based on this experimental data, what is the probability that a bulb selected at random is not defective?

A fair six-sided die is rolled once. What is the theoretical probability of getting a prime number?

In a bag of 20 candies, 5 are red, 7 are blue, and the rest are green. If one candy is chosen at random, find the probability that it is not blue.

A spinner is divided into 8 equal sectors, numbered 1 to 8. If the spinner is spun twice, find the theoretical probability that the sum of the two numbers is exactly \( 15 \).

A fair six-sided die is rolled once. What is the theoretical probability of obtaining a prime number?

A fair six-sided die is rolled 120 times.

(a) Calculate the theoretical probability of rolling a number greater than 4 in a single roll.
(b) Based on the theoretical probability, find the expected frequency of rolling a number greater than 4 in 120 rolls.
(c) If the number 5 or 6 actually appears 45 times in the 120 rolls, state the experimental probability of rolling a number greater than 4.

A bag contains a number of red, blue, and yellow counters. A counter is chosen at random, its color noted, and then replaced. In an experiment, this procedure is repeated 80 times, and the frequencies are recorded as follows: Red = 28, Blue = 36, Yellow = 16.

(a) Find the experimental probability of obtaining a blue counter.
(b) If the bag actually contains a total of 15 counters, and the theoretical probability of drawing a yellow counter is \( \frac{1}{5} \), find the exact number of yellow counters in the bag.
(c) If the experiment is repeated for a total of 500 trials instead of 80 trials, find the expected frequency of obtaining a yellow counter based on its theoretical probability.