Discrete Math: Discrete Probability

Suppose a beverage manufacturer adds gold flakes into a beverage at a rate of 800 flakes per litre. Given a 10 millilitre sample taken from a well-shaken 1 litre bottle, what is the probability that the sample contains exactly 2 flakes of gold?

A European roulette wheel has 18 red slots, 18 black slots, and 1 green slot. What is the probability that the first time the ball lands in a red slot occurs on the 5th spin?

Sarah is deciding which courses she wants to take in her next college semester. The probability that she enrolls in an algebra course is 0.3 and the probability that she enrolls in a biology course is 0.7. The probability that she will enroll in an algebra course given that she enrolls in a biology course is 0.4.

Part A: What is the probability that she will enroll in both an algebra course and a biology course?

Part B: What is the probability that she will enroll in an algebra course or a biology course?

Part C: Are the two events independent?

Part D: Are the two events mutually exclusive?

Suppose that 60% of American adults approve of the way the president is handling his job, and we randomly sample two American adults. Let the random variable X represent the number of those adults that approve. X can take on the values 0, 1, or 2. Calculate the mean and the variance of this probability distribution.

Let X represent the number of heads when this coin is tossed twice. Here's the probability distribution of X. Suppose we want to calculate the expectation of the random variable X.

How can you create a mathematical function that contains all the information about probabilities associated with a dice, such that we can recover all property values from P1 to P6?

A sample contains a certain amount of bacteria. The bacteria doubles every 20 minutes. At this rate, how many counts of bacteria will there be in 3 hours?

How many ways can you roll an even number on a die or draw a face card?

A bag consists of 8 red marbles, 7 blue marbles, 6 green marbles, and 4 yellow marbles. What is the probability of selecting a red marble?

What is the probability of selecting a blue marble on the first try and then a green marble on the second try with replacement?

What is the probability of selecting a yellow marble on the first try and then a red marble on the second try without replacement?

What is the probability of selecting two blue marbles with replacement?

What is the probability of selecting two green marbles without replacement?

If you roll a 6-sided die and flip a coin, what is the probability of rolling a 5 and getting heads?

What is the probability of drawing two green marbles without replacement?