Statistics 101 Ch. 4

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What is the formula to calculate P(A ?)?
P(A ?) = 1 - P(A)
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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
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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
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The ____________ for a procedure consists of all possible simple events or all outcomes that cannot be broken down any further.
sample space
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The classical approach to probability requires that the outcomes are _______
equally likely.
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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
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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)
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When using the ____________ always be careful to avoid double-counting outcomes.
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Events that are ____________ cannot occur at the same time.
disjoint
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____________events are mutually exclusive and cannot occur at the same time.
Disjoint
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________ indicates the probability that in a single trial, event A occurs, event B occurs, or they both occur.
P(A or B)
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The _____________ event A occuring are the ratio P (A) / P(A ?)
actual odds in favor of
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How else can we express P(A) / P(A ?)
a:b or (a to b)
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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.
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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.
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The _____________ of an event is the event not occurring. How is it denoted?
Complement. A ?
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P(A) + P(A ?) = 1 is one way to express___________.
rule of complementary events.
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___________ represents the probability of event B occurring, given that event A has already occurred.
P (B|A)
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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
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____________is associated with multiplication when computing probabilities?
And
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A picture of line segments branching out from one starting point illustrating the possible outcomes of a procedure is called a _______________.
tree diagram.
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What does P(B|A) represent?
The probability of event B occurring after it is assumed that event A has already occurred.
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Two events A and B are ___________ if the occurrence of one does not affect the probability of the occurrence of the other.
independent
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Selections made with replacement are considered to be ________________.
independent.
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"At least one" is equivalent to_________.
:one or more."
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The complement of "at least one" is________
"none"
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A _______ probability of an event is a probability obtained with knowledge that some other event has already occurred.
conditional
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Confusion of the inverse occurs when we incorrectly believe___________.
P(B|A) = P(A|B)
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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.
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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.
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____________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.
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_______________(!) 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
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0! = _
1
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9! = ___________________
= 9 * 8 * 7 ....1
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____________ 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
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What are the rules for permutations?