Statistics 101 Ch. 4

____________is associated with multiplication when computing probabilities?

And

A _______ probability of an event is a probability obtained with knowledge that some other event has already occurred.

conditional

What is the formula to find permutations?

nPr = n! / (n-r)!

The complement of "at least one" is________

"none"

0! = _

1

_______________(!) states that n! is the number of different permutations (order counts) of n different items when all n of them are selected.

The factorial rule

Which of the following values cannot be probabilities? 1) .05, -0.41, 1, 0, 3/5, 1.22, √2, 5/3 2) Why?

1. -.41, 1.22, √2 and 5/3 2. Because the probability of A is between 0 and 1 inclusive. or 0 ≤ P(A) ≤ 1

"At least one" is equivalent to_________.

:one or more."

If the order of the items selected matters, then we have _______________.

permutation problem.

P(A) + P(A ̅) = 1 is one way to express___________.

rule of complementary events.

What is wrong with the expression P(A) + P(A ̅) - 0.5?

Based on the rule of complements, the sum of P(A) and P(A ̅) must always be 1, so the sum cannot be 0.5.

In horse racing, a trifecta is a bet that the first three finishes in a race are selected, and they are selected in the correct order. Does a trifecta involve combinations or permutations? Expliain.

Because the order of the first three finishers does make a differences, the trifecta involves permutations.

The _____________ of an event is the event not occurring. How is it denoted?

Complement. A ̅

____________events are mutually exclusive and cannot occur at the same time.

Disjoint

___________ represents the probability of event B occurring, given that event A has already occurred.

P (B|A)

________ indicates the probability that in a single trial, event A occurs, event B occurs, or they both occur.

P(A or B)

What is the formula to calculate P(A ̅)?

P(A ̅) = 1 - P(A)

What is the formula to find P(A) for a series of simple events (ex: tossing a coin and selecting a number at the same time)

P(A) = # of ways A can occur / number of diff simple events = s / n

Confusion of the inverse occurs when we incorrectly believe___________.

P(B|A) = P(A|B)

____________ states that the number of different combinations (order does not count) when n different items are available, but only r of them are selected without replacement, is given by: nCr = n! / (n-r) !r!

The combinations rule

____________states given that the first event can occur m ways and the second event can occur n ways, the number of ways that the two events can occur is given by the following formul. m*n

The fundamental counting rule.

A procedure is repeated again and again, the relative frequency of an event tends to approach the actual probability. This is known as ______________.

The law of large numbers

What does P(B|A) represent?

The probability of event B occurring after it is assumed that event A has already occurred.

Events that are ____________ cannot occur at the same time.

disjoint

The classical approach to probability requires that the outcomes are _______

equally likely.

Two events A and B are ___________ if the occurrence of one does not affect the probability of the occurrence of the other.

independent

Selections made with replacement are considered to be ________________.

independent.

9! = ___________________

= 9 * 8 * 7 ....1

How else can we express P(A) / P(A ̅)

a:b or (a to b)

Are following events disjoint? 1. Randomly selecting someone who is married. 2. Randomly selecting someone who is a bachelor.

Yes, since they cannot occur at the same time.

The _____________ event A occuring are the ratio P (A) / P(A ̅)

actual odds in favor of

When using the ____________ always be careful to avoid double-counting outcomes.

addition rule

The conditional property of B given A can be found by __________.

assuming that event A has occurred, and then calculating the probability that even B will occur.

The ____________ for a procedure consists of all possible simple events or all outcomes that cannot be broken down any further.

sample space

For a sequence of two events in which the first event can occur m ways and the second event can occur n ways, the events together can occur a total of m n ways. This is called_____________.

the fundamental counting rule.

A picture of line segments branching out from one starting point illustrating the possible outcomes of a procedure is called a _______________.

tree diagram.

What are the rules for permutations?

1. Items must be unique. (n different items, total #) 2. r: The items to be arranged out of n 3. Arrangement/order matters

The _________________ states that if calculatuions are very cumbersome and if the sample size is no more than 5% of the size of the population, treat the selections as being independent.

5% guideline

Which of the following is NOT a principle of probability? A) The probability of any event is between 0 and 1 inclusive. B) All events are equally likely in any probability procedure. C) The probability of an event that is certain to occur is 1. D) The probability of an impossible event is 0.

B)