Introduction to Probability Theory

True (A)

S or Ω

<p>{ HH , HT, TH, TT }</p> Signup and view all the answers

<p>Random experiment = An experiment with unpredictable outcomes Sample space = Set of all possible outcomes Event = A subset of the sample space Probability = A measure of uncertainty in outcomes</p> Signup and view all the answers

<p>Data communication systems (B)</p> Signup and view all the answers

<p>True (A)</p> Signup and view all the answers

<p>Calculating conditional probabilities</p> Signup and view all the answers

<p>0.75 (B)</p> Signup and view all the answers

<p>False (B)</p> Signup and view all the answers

<p>Independent events are those events whose occurrence is not dependent on any other event.</p> Signup and view all the answers

<p>B</p> Signup and view all the answers

<p>Choosing a card without replacement = Dependent Events Tossing a coin = Independent Events Rolling a die = Independent Events Not paying a bill and losing power = Dependent Events</p> Signup and view all the answers

<p>0 (B)</p> Signup and view all the answers

<p>False (B)</p> Signup and view all the answers

<p>0 ≤ P(A) ≤ 1 (C)</p> Signup and view all the answers

<p>3/8</p> Signup and view all the answers

<p>False (B)</p> Signup and view all the answers

<p>null</p> Signup and view all the answers

<p>P(A ∪ B) = P(A) + P(B)</p> Signup and view all the answers

<p>nA/n</p> Signup and view all the answers

<p>1/2 (A)</p> Signup and view all the answers

<p>False (B)</p> Signup and view all the answers

<p>Axiomatic Definition = Based on assumptions about probability Relative-Frequency Definition = Based on experimental occurrences Classical Definition = Based on equally likely outcomes</p> Signup and view all the answers

<p>6 (D)</p> Signup and view all the answers

<p>5</p> Signup and view all the answers

<p>True (A)</p> Signup and view all the answers

<p>0.12 or 3/25</p> Signup and view all the answers

<p>{1, 2, 3, 4, 6, 7} (B)</p> Signup and view all the answers

<p>False (B)</p> Signup and view all the answers

<p>{2, 7}</p> Signup and view all the answers

<p>disjoint</p> Signup and view all the answers

<p>P(A | B) = P(A ∩ B) / P(B) (B)</p> Signup and view all the answers

<p>False (B)</p> Signup and view all the answers

<p>1/2</p> Signup and view all the answers

The set of all possible outcomes of a random experiment.

Any subset of the sample space.

An experiment with uncertain outcomes.

Branch of math studying random phenomena.

To model and understand systems with uncertainty.

Events with unpredictable outcomes repeated.

Coin flips: {HHH, HHT, HTH, HTT, THH, THT, TTH, TTT}

Getting a heads: {H} from an example series of coin flips

Probability calculated as the ratio of favorable outcomes to total possible outcomes.

Events that have the same chance of occurring.

An individual member of a set.

A set contained within another set, where all its elements are also elements of the larger set.

The set containing all possible elements.

The set containing no elements.

The set containing all elements NOT in the original set within the universal set.

Events whose outcomes are influenced by previous events.

Events whose outcomes are not affected by previous events.

The probability of an event happening given that another event has already occurred.

A formula to calculate conditional probability, relating the probability of an event to its condition.

Choosing a card from a deck without replacing it, then choosing another card.

Defines probability based on three axioms that describe the behavior of probabilities, including the range of probability values, the probability of the entire sample space, and how probabilities of mutually exclusive events combine.

The probability of any event must be between 0 and 1, inclusive. 0 means the event is impossible, and 1 means it's certain.

The probability of the entire sample space (all possible outcomes) is 1, meaning something must happen.

For mutually exclusive events (events that cannot happen simultaneously), the probability of one event occurring OR the other is the sum of their individual probabilities.

Defines the probability of an event as the limit of the ratio of the number of times the event occurs to the total number of trials, as the number of trials approaches infinity.

The relative frequency definition is not always practical because some experiments cannot be repeated infinitely, and the limit might not exist.

It is applicable when the experiment can be repeated many times and the limit of the relative frequency exists and tends to a finite value.

Defines the probability of an event as the ratio of the number of favorable outcomes to the total number of equally likely outcomes.

The set of all elements found in either set A or set B, including elements shared by both.

The set of all elements that are common to both set A and set B.

The set of elements in set A that are not present in set B.

Sets that have no elements in common.

The order of sets in a union doesn't matter. A ∪ B is the same as B ∪ A.

The grouping of sets in a union doesn't matter. A ∪ (B ∪ C) is the same as (A ∪ B) ∪ C.

The probability of an event occurring given that another event has already happened.

P(A|B) = P(A ∩ B) / P(B), where P(A|B) is the probability of event A given event B has occurred.