Mathematics: Probability and Statistics

A _____________ is similar to a permutation, except that the order in which the objects are selected does not matter.

Combination.

The mathematical operation for calculating permutations is called a ____________.

Factorial. A factorial is represented by an exclamation mark:3! = 3 * 2 * 1 = 67! = 7 * 6 * 5 * 4 * 3 * 2 * 1 = 5,040

What is the probability (as a fraction) that a card drawn at random from a deck of cards will be an ace? ______

4/52. Since of the 52 cards in the deck, 4 are aces, the probability is 4/52. In general, the probability of an event is the number of favorable outcomes divided by the total number of possible outcomes. (This assumes the outcomes are all equally likely.) In this case there are four favorable outcomes: (1) the ace of spades, (2) the ace of hearts, (3) the ace of diamonds, and (4) the ace of clubs. Since each of the 52 cards in the deck represents a possible outcome, there are 52 possible outcomes.

Whenever we want to find the probability of event A or event B occurring, we _______ the probability of event A occurring to the probability of event B occurring, and then subtract the probability of both A and B occurring.

Add. This is called the general addition rule:P(A ∪ B) = P(A) + P(B) - P(A ∩ B)

Permutation means____________ of things.

Arrangemant. The word arrangement is used, if the order of things is considered.

By using the ______________ rule, we can figure out the probability of an event happening if given the probability of the event not happening (and vice versa).

Complement. Since we know that an event is guaranteed to either happen or not happen, P(A ∪ A') = 1. In other words, the chance that an event or its complement will happen is 1.

The _______ is a measure of central tendency that calculates an average value for all the observed values.

Mean. Mean is usually synonymous with average. To calculate the mean, we add the values of all the observations and then divide the sum by the total number of observations.

The _________ is the middle value of several readings, where all those given readings are placed in an increasing order.

Median. Let's say you're given a list of track times in minutes: 20, 35, 30, 25, 20.

A ______________ is an ordered arrangement of a group of objects.

Permutation. Order is important in a permutation; therefore, permutations with the same objects in a different order are considered distinct arrangements. Some of the objects in the set, as well in a permutation, may be indistinguishable from one another.

The ______________ of an event is the measure of the chance that the event will occur as a result of an experiment.

Probability. The probability of an event A is the number of ways event A can occur divided by the total number of possible outcomes. The probability of an event A, symbolized by P(A), is expressed as a fraction or a decimal from 0 to 1. Events that are unlikely will have a probability near 0, and events that are likely to happen have probabilities near 1. If P(A) > P(B) then event A is more likely to occur than event B. If P(A) = P(B) then events A and B are equally likely to occur.

Combination means ____________ of things.

Selection. The word selection is used, when the order of things has no importance. To find the combinations of things you multiply.