Probability

A bag contains 6 red marbles, 5 blue marbles, and 4 green marbles. If one marble is selected at random, what is the probability that it is green?

A box contains 7 white balls and 5 black balls. Two balls are drawn without replacement. What is the probability that both balls are white?

A card is drawn at random from a standard 52-card deck. What is the probability of drawing a queen or a spade?

A disease affects 2% of a population. A medical test correctly gives a positive result for 95% of people who have the disease and gives a false positive result for 5% of people who do not have the disease. If a randomly selected person tests positive, what is the probability that the person actually has the disease?

A fair six-sided die is rolled twice. What is the probability of rolling a 6 on both rolls?

A game costs $4 to play. A player rolls a fair six-sided die. If the player rolls a 6, the player receives $15; otherwise, the player receives nothing. Find the expected net gain or loss per game.

A security code consists of 4 different digits selected from 0 through 9. No digit may be repeated. How many different codes are possible?

How many different 3-person committees can be selected from a group of 8 people?

In a class of 30 students, 18 study mathematics, 12 study physics, and 8 study both mathematics and physics. If a student is selected at random from those who study mathematics, what is the probability that the student also studies physics?

The probability that a student passes an exam is 0.82. What is the probability that the student does not pass the exam?