question

What is the formula to calculate P(A ?)?

answer

P(A ?) = 1 - P(A)

question

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

answer

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

question

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)

answer

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

question

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

answer

sample space

question

The classical approach to probability requires that the outcomes are _______

answer

equally likely.

question

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

answer

The law of large numbers

question

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.

answer

B)

question

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

answer

addition rule

question

Events that are ____________ cannot occur at the same time.

answer

disjoint

question

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

answer

Disjoint

question

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

answer

P(A or B)

question

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

answer

actual odds in favor of

question

How else can we express P(A) / P(A ?)

answer

a:b or (a to b)

question

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

answer

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.

question

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

answer

Yes, since they cannot occur at the same time.

question

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

answer

Complement. A ?

question

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

answer

rule of complementary events.

question

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

answer

P (B|A)

question

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.

answer

5% guideline

question

____________is associated with multiplication when computing probabilities?

answer

And

question

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

answer

tree diagram.

question

What does P(B|A) represent?

answer

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

question

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

answer

independent

question

Selections made with replacement are considered to be ________________.

answer

independent.

question

"At least one" is equivalent to_________.

answer

:one or more."

question

The complement of "at least one" is________

answer

"none"

question

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

answer

conditional

question

Confusion of the inverse occurs when we incorrectly believe___________.

answer

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

question

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

answer

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

question

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.

answer

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

question

____________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

answer

The fundamental counting rule.

question

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

answer

The factorial rule

question

0! = _

answer

1

question

9! = ___________________

answer

= 9 * 8 * 7 ....1

question

____________ 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!

answer

The combinations rule

question

What are the rules for permutations?

answer

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

question

What is the formula to find permutations?

answer

nPr = n! / (n-r)!

question

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_____________.

answer

the fundamental counting rule.

question

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

answer

permutation problem.