Sample Spaces：练习题

A bag contains three balls of different colours: red (R), green (G), and blue (B). Two balls are drawn one after another with replacement. Which of the following sets correctly represents the sample space of this experiment?

A fair six-sided die is rolled twice. Let \( S \) be the sample space of all possible outcomes. Let event \( A \) be the event that the sum of the two numbers is a prime number, and event \( B \) be the event that the product of the two numbers is a multiple of 4. Find the number of outcomes in the set \( A \cap B \).

Two fair coins are tossed simultaneously. What is the total number of outcomes in the sample space?

A fair six-sided die is rolled once. Find the probability of obtaining a prime number. List the sample space first.

Two fair coins are tossed at the same time. Using a tree diagram or a list, determine the sample space and find the probability of obtaining at least one Head.

A spinner is divided into four equal sectors colored Red, Blue, Yellow, and Green. List the sample space of the outcomes when the spinner is spun once.

Two fair four-sided dice (numbered 1 to 4) are rolled.
(a) List all possible outcomes in the sample space using a table or coordinates.
(b) Find the probability that the sum of the two dice is 5.