Discrete Probability Distributions

Front

What is a discrete probability distribution?

Back

A discrete probability distribution is a statistical distribution that describes the likelihood of obtaining the possible values that a discrete random variable can take.

Tags

CCSS.HSS.MD.A.3

CCSS.HSS.MD.A.4

Front

What is a random variable?

Back

A random variable is a variable whose possible values are numerical outcomes of a random phenomenon.

Front

Define the term 'probability'.

Back

Probability is a measure of the likelihood that an event will occur, expressed as a number between 0 and 1.

Tags

CCSS.7.SP.C.5

Front

What is the formula for calculating the probability of exactly k successes in n trials?

Back

P(X = k) = (n choose k) * p^k * (1-p)^(n-k), where p is the probability of success.

Tags

CCSS.HSS.MD.A.3

CCSS.HSS.MD.A.4

Front

What does 'n choose k' mean in probability?

Back

'n choose k' (denoted as C(n, k) or nCk) is the number of ways to choose k successes from n trials, calculated as n! / (k!(n-k)!).

Front

What is the probability of getting at least 4 correct answers on a 5-question true-false quiz?

Back

The probability of getting at least 4 correct answers is the sum of the probabilities of getting exactly 4 and exactly 5 correct answers.

Front

How do you calculate the probability of getting exactly 4 correct answers on a 5-question quiz?

Back

P(X = 4) = C(5, 4) * (0.5)^4 * (0.5)^(5-4) = 5 * 0.0625 * 0.5 = 0.15625.

Front

What is the probability of getting exactly 5 correct answers on a 5-question quiz?

Back

P(X = 5) = C(5, 5) * (0.5)^5 * (0.5)^(5-5) = 1 * 0.03125 * 1 = 0.03125.

Front

What is the total probability of getting at least 4 correct answers?

Back

Total probability = P(X = 4) + P(X = 5) = 0.15625 + 0.03125 = 0.1875.

Tags

CCSS.HSS.CP.B.7

Front

What is the expected value of a discrete random variable?

Back

The expected value is the long-term average value of repetitions of the experiment it represents, calculated as E(X) = Σ [x * P(x)].

Tags

CCSS.HSS.MD.A.2