Probability of an Event: Practice Questions

A bag contains 4 red balls, 5 blue balls, and 3 green balls. If a ball is drawn at random from the bag, what is the probability that the ball is not red?

A bag contains 4 red balls, 3 blue balls, and some green balls. If a ball is selected at random from the bag and the probability of picking a blue ball is \(\frac{1}{4}\), how many green balls are there in the bag?

Ten cards, numbered \(1\) to \(10\), are placed in a box. Three cards are drawn at random from the box simultaneously. What is the probability that the product of the numbers on the three cards is a multiple of \(10\)?

Two fair six-sided dice are rolled simultaneously. What is the probability that the sum of the two numbers shown is a prime number?

In a group of 40 students, 25 students like Mathematics, 20 like Science, and 10 like both subjects. If a student is chosen at random from the group, what is the probability that the student likes neither Mathematics nor Science?

A fair six-sided die is rolled once. Let \( A \) be the event of rolling an even number and \( B \) be the event of rolling a prime number.

(a) List the possible outcomes for event \( A \) and calculate the probability \( P(A) \).
(b) List the possible outcomes for event \( B \) and calculate the probability \( P(B) \).
(c) Identify the outcome(s) that belong to both event \( A \) and event \( B \). Calculate the probability of rolling a number that is both even and prime.