Algebra Probability Mock Tests

In a class, 60% of students are girls and 40% are boys. Among girls, 50% wear glasses; among boys, 2/3 wear glasses. If a randomly selected student wears glasses, the probability that the student is a girl is:

A bag contains 3 red and 5 blue balls. Another bag contains 5 red and 3 blue balls. One ball is drawn from each bag. Given that the two balls are of different colours, the probability that the first ball is red is

A bag A contains 3 red and 5 blue balls. Bag B contains 5 red and 3 blue balls. One ball is drawn from each bag. Given that the two balls are of different colours, the probability that the ball from bag A is red is

Three identical boxes contain coins. Box I has two gold coins, Box II has two silver coins, and Box III has one gold and one silver coin. A box is chosen at random, and a coin is drawn from it. The coin drawn is gold. The probability that the other coin in the box is also gold is:

Three dice are rolled simultaneously. Let E₁, E₂, E₃ be the events that the first, second, and third die shows an even number respectively. Let A be the event that exactly two dice show even numbers. Then P(A) is:

A bag contains 3 red and 5 black balls. Another bag contains 4 red and 3 black balls. One ball is drawn at random from the first bag and placed into the second bag. Then one ball is drawn from the second bag. The probability that this ball is red is

Three boxes contain: Box A: 2 red, 2 black; Box B: 3 red, 1 black; Box C: 1 red, 3 black. A box is chosen at random and a red ball is drawn. The probability that the ball came from Box B is:

Two players A and B take turns rolling a fair die in the order A → B → A → B → ... The first player to roll a 6 wins. The probability that A wins is: