Probability：練習問題

A bag contains 4 red marbles, 5 blue marbles, and 3 green marbles. If a marble is chosen at random from the bag, find the probability that it is not blue.

Two fair six-sided dice are rolled and the numbers on the top faces are added together. What is the probability that the sum is a prime number less than 6?

A bag contains 4 red counters, 3 blue counters, and 2 green counters. Three counters are drawn at random from the bag without replacement. Find the probability that all three counters are of different colours.

A bag contains 8 red balls, 5 blue balls, and 7 green balls. A ball is picked at random. What is the probability that the ball is not blue?

A bag contains 6 red marbles and 4 blue marbles. Two marbles are drawn at random one after another without replacement. Find the probability that the first marble is red and the second marble is blue.

A box contains 5 red, 8 blue, and 7 green pens. If one pen is chosen at random, find the probability that the pen is not blue.

A bag contains 4 red marbles and 6 green marbles. Two marbles are drawn at random one after another without replacement.
(a) Draw a tree diagram to represent all possible outcomes and their probabilities.
(b) Calculate the probability that both marbles are of the same color.
(c) Calculate the probability that at least one marble is red.

A bag contains 7 red balls and 3 white balls. Two balls are drawn from the bag at random, one after another, without replacement.

(a) Find the probability that both balls drawn are of the same color.
(b) Find the probability that at least one of the balls drawn is white.
(c) If this experiment is repeated but the first ball is replaced before the second ball is drawn, calculate the new probability that both balls are of the same color.