4H MC

Front

What is the probability of finding an item that must be removed in a bag pulled aside for inspection?

Back

The probability is 2 out of 5, or 0.4.

Front

What is the formula for calculating the probability of at least k successes in a binomial distribution?

Back

P(X ≥ k) = 1 - P(X < k) = 1 - Σ (n choose x) * p^x * (1-p)^(n-x) for x = 0 to k-1.

Front

Define a binomial distribution.

Back

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

Front

What are the parameters of a binomial distribution for 20 multiple choice questions with 4 choices each?

Back

n = 20 (number of questions), p = 0.25 (probability of guessing correctly).

Front

What does P(X=1) represent in a probability distribution?

Back

P(X=1) represents the probability of exactly 1 success in the given number of trials.

Front

How do you calculate the probability of rolling a specific number on a die?

Back

The probability of rolling a specific number on a fair die is 1 divided by the number of sides on the die.

Front

What is the expected value in a binomial distribution?

Back

The expected value (mean) is calculated as E(X) = n * p.

Front

What is the variance in a binomial distribution?

Back

The variance is calculated as Var(X) = n * p * (1 - p).

Front

What is the probability of rolling a 7 exactly 3 times in 10 rolls of an eight-sided die?

Back

Use the binomial probability formula: P(X=k) = (n choose k) * p^k * (1-p)^(n-k), where n=10, k=3, and p=1/8.

Front

What is the complement rule in probability?

Back

The complement rule states that the probability of an event occurring is equal to 1 minus the probability of the event not occurring.