Probability4 (Permutations and Combinations, Expected Value)

Front

What is the formula for Combinations?

Back

The formula for Combinations is \( \frac{n!}{(n-r)! r!} \)

Front

What is the expected value of a random variable?

Back

The expected value is calculated as \( E(X) = \sum (X \cdot P(X)) \), where X is the value and P(X) is the probability.

Front

What is the formula for Permutations?

Back

The formula for Permutations is \( \frac{n!}{(n-r)!} \)

Front

How many possible three-digit area codes can be created if the first digit can be 2-9, the second digit can be 0 or 1, and the third digit can be 0-9?

Back

There are 160 possible area codes.

Front

What is the probability that Joe will go second and Beth will go last among five comedians?

Back

The probability is \( \frac{1}{20} \)

Front

Define Permutations in the context of probability.

Back

Permutations refer to the arrangement of objects in a specific order, where the order matters.

Front

Define Combinations in the context of probability.

Back

Combinations refer to the selection of objects without regard to the order, where the order does not matter.

Front

What is the difference between Permutations and Combinations?

Back

Permutations consider the order of selection, while Combinations do not.

Front

How do you calculate the expected value from a probability distribution?

Back

Multiply each outcome by its probability and sum the results.

Front

What is the factorial of a number n (n!)?

Back

The factorial of n is the product of all positive integers up to n.