Probability MC Practice - Chapter 6

Front

What is a binomial distribution?

Back

A binomial distribution is a probability distribution that summarizes the likelihood that a value will take one of two independent outcomes under a given number of trials. It is defined by two parameters: n (number of trials) and p (probability of success).

Front

What is a geometric distribution?

Back

A geometric distribution models the number of trials needed to get the first success in a series of independent Bernoulli trials, each with the same probability of success. It is characterized by a single parameter p (probability of success).

Front

What is the difference between binomial and geometric distributions?

Back

The key difference is that a binomial distribution has a fixed number of trials (n), while a geometric distribution continues until the first success occurs, meaning the number of trials is variable.

Front

What does it mean for random variables X and Y to be independent?

Back

Two random variables X and Y are independent if the occurrence of one does not affect the probability of the occurrence of the other. This means P(X and Y) = P(X) * P(Y).

Front

How do you calculate the expected value of a random variable?

Back

The expected value (E) of a random variable is calculated by summing the products of each possible value and its corresponding probability: E(X) = Σ [x * P(x)].

Front

What is the formula for calculating the expected profit in a business scenario?

Back

The expected profit is calculated by multiplying each outcome by its probability and summing these products: E(Profit) = (Profit1 * P1) + (Profit2 * P2) + ... + (ProfitN * PN).

Front

What is the probability of getting a red card from a standard deck of cards?

Back

In a standard deck of 52 cards, there are 26 red cards (hearts and diamonds). Therefore, the probability of drawing a red card is P(red) = 26/52 = 0.5.

Front

What is the significance of replacing a card in probability experiments?

Back

Replacing a card ensures that the total number of cards remains constant, which keeps the probabilities the same for each draw. This is essential for maintaining a binomial distribution.

Front

What does it mean for a distribution to be skewed?

Back

A distribution is skewed if it is not symmetrical. A right-skewed distribution has a longer tail on the right side, while a left-skewed distribution has a longer tail on the left side.

Front

What is the probability of success in a binomial distribution?

Back

The probability of success (p) in a binomial distribution is the likelihood of achieving a successful outcome in a single trial, which remains constant across all trials.