Probability4 (Permutations and Combinations, Expected Value)

Front

What is the probability of an event occurring?

Back

The probability of an event is a measure of the likelihood that the event will occur, expressed as a number between 0 and 1, where 0 indicates impossibility and 1 indicates certainty.

Front

What is a permutation?

Back

A permutation is an arrangement of objects in a specific order. The number of permutations of n objects taken r at a time is given by n! / (n - r)!.

Front

What is a combination?

Back

A combination is a selection of items from a larger set where the order does not matter. The number of combinations of n objects taken r at a time is given by n! / (r!(n - r)!).

Front

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

Back

The expected value (E) is calculated by multiplying each possible outcome by its probability and summing all these products: E(X) = Σ [x * P(x)].

Front

What is the formula for calculating permutations?

Back

The formula for permutations is n! / (n - r)!, where n is the total number of items, and r is the number of items to arrange.

Front

If a coin is flipped, what is the probability of getting heads?

Back

The probability of getting heads when flipping a fair coin is 1/2.

Front

What is the expected value of Eva's coin flip if she wins $4 for heads and loses $3 for tails?

Back

The expected value is calculated as (0.5 * 4) + (0.5 * -3) = $0.50.

Front

What is the total number of ways to choose 2 women from a group of 4?

Back

The total number of ways to choose 2 women from 4 is given by the combination formula: C(4, 2) = 4! / (2!(4 - 2)!) = 6.

Front

What is the probability that Joe will go second in a show with 5 comedians?

Back

The probability that Joe will go second is 1/5.

Front

What is the expected value of a random variable with outcomes 50, 20, and 5 with probabilities 0.1, 0.3, and 0.6 respectively?

Back

The expected value is calculated as (50 * 0.1) + (20 * 0.3) + (5 * 0.6) = 14.