Permutations & Combinations & Probability of Compound Events

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 objects without regard to the order. The number of combinations of n objects taken r at a time is given by n! / (r! * (n - r)!).

Front

What is the formula for calculating the probability of an event?

Back

The probability of an event is calculated as P(E) = Number of favorable outcomes / Total number of outcomes.

Front

How do you calculate the probability of compound events?

Back

For independent events, P(A and B) = P(A) * P(B). For dependent events, P(A and B) = P(A) * P(B|A).

Front

What is the total number of outcomes when flipping a coin and drawing a marble from a bag?

Back

The total number of outcomes is the product of the outcomes of each event. For a coin (2 outcomes) and a bag with 9 marbles (9 outcomes), total outcomes = 2 * 9 = 18.

Front

How many ways can 3 different vases be arranged?

Back

The number of arrangements (permutations) of 3 different vases is 3! = 6.

Front

How many ways can a president, vice president, and treasurer be elected from 40 students?

Back

The number of ways to elect 3 officers from 40 students is 40 * 39 * 38 = 59,280.

Front

What is the probability of drawing a blue marble from a bag of 9 marbles?

Back

The probability of drawing a blue marble is P(Blue) = Number of blue marbles / Total marbles = 2/9.

Front

What is the probability of flipping heads on a fair coin?

Back

The probability of flipping heads is P(Heads) = 1/2.

Front

How do you find the probability of two independent events occurring together?

Back

Multiply the probabilities of each event: P(A and B) = P(A) * P(B).