MTH281: Probability Chapter 3 Quiz

True (A)

The fundamental counting principle states that if an event can occur in 'm' ways and another independent event can occur in 'n' ways, then the two events can occur in 'm*n' ways.

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

<p>Sample Space = The set of all possible outcomes of a random experiment. Event = A subset of the sample space, representing a specific outcome or set of outcomes. Probability of an Event = The likelihood of an event occurring, expressed as a number between 0 and 1. Conditional Probability = The probability of an event occurring given that another event has already occurred.</p> Signup and view all the answers

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

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

<p>The probability of both events A and B occurring simultaneously.</p> Signup and view all the answers

<p>double counting</p> Signup and view all the answers

<p>P(A) = Probability of event A happening P(B) = Probability of event B happening P(A and B) = Probability of both event A and event B happening simultaneously P(A or B) = Probability of either event A or event B happening, or both</p> Signup and view all the answers

<p>Calculating the area of a rectangle (B)</p> Signup and view all the answers

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

<p>{1, 2, 3, 4, 5, 6}</p> Signup and view all the answers

<p>probability experiment</p> Signup and view all the answers

<p>Examining a fuse for a defect = {N , D} Examining two fuses in sequence = {N N , N D, DN , DD} Genders of three children from oldest to youngest = {BBB, BBG, BGB, BGG, GBB, GBG, GGB, GGG} Running a computer program = {compiles, does not compile}</p> Signup and view all the answers

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

<p>event A</p> Signup and view all the answers

<p>Determining the number of students in a class (D)</p> Signup and view all the answers

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

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

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

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

<p>Complement Rule = P(A') = 1 - P(A) Addition Rule = P(A or B) = P(A) + P(B) - P(A and B) Multiplication Rule = P(A and B) = P(A) * P(B|A)</p> Signup and view all the answers

<p>Conditional probability of event A given that event B has already occurred</p> Signup and view all the answers

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

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

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

<p>Events that have no outcomes in common. (A)</p> Signup and view all the answers

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

<p>0.69 (B)</p> Signup and view all the answers

<p>The probability of a homeowner purchasing a smart device to monitor energy consumption</p> Signup and view all the answers

<p>mutually exclusive</p> Signup and view all the answers

<p>P(A') = 1 - P(A) = 1 - 0.45 = 0.55</p> Signup and view all the answers

<p>0.60 (A)</p> Signup and view all the answers

<p>0.9</p> Signup and view all the answers

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

<p>0.9761</p> Signup and view all the answers

<p>Probability of at least one of three rotator cuff surgeries being successful = 1 - P(none of the surgeries are successful) Probability of a system working with three computers, if it requires all three computers to be functional = P(computer 1 works) * P(computer 2 works) * P(computer 3 works) Probability of two fuses being defective, selected without replacement from a box with 20 fuses (5 are defective) = P(first fuse defective) * P(second fuse defective given the first was defective)</p> Signup and view all the answers

<p>5/20 * 4/19 (D)</p> Signup and view all the answers

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

<p>both blocks having an error</p> Signup and view all the answers

The set of all possible outcomes of a probability experiment.

A specific outcome or collection of outcomes from a sample space.

The probability of an event not occurring is 1 minus the probability of the event occurring.

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

Two events are independent if the occurrence of one does not affect the probability of the other.

A probability rule for finding the likelihood of A or B occurring.

The probability that event A or event B occurs.

The probability of event A occurring.

The probability of event B occurring.

The probability that both events A and B occur simultaneously.

A process of observation with uncertain outcomes, where one outcome occurs each time.

A method to determine the total number of outcomes by multiplying the number of choices for each event.

Two events are independent if the occurrence of one does not affect the other.

Used to find the joint probability of two independent events both occurring.

The likelihood of an event occurring, expressed as a number between 0 and 1.

The probability that in a group, at least two share a birthday.

A password that contains only consonants, no vowels.

The chance that a selected password includes at least one odd number among the digits.

Two events are independent if the occurrence of one does not affect the other.

Events that cannot happen at the same time; if one occurs, the other cannot.

Events that can occur at the same time; one does not exclude the possibility of the other.

The likelihood of an event occurring, usually expressed as a number between 0 and 1.

The probabilities of events A and B occurring, individually.

The probability that event A does not occur, calculated as 1 - P(A).

The rule that helps calculate the probability of either event A or event B occurring.

Use of probability concepts in relatable situations, like homeowner device purchases.

The probability that a patient sues when diagnosed incorrectly is 0.9.

First block error probability is 0.25 and second block is 0.35.

The probability of successful rotator cuff surgery is 0.9.

Calculating success rates for multiple surgeries using independent probabilities.

Probability that all computers in a system work together is calculated using their individual success rates.

Probability that at least one computer works in a system of three.

Calculating the probability that both selected fuses are defective without replacement.

Calculating the probability that both selected fuses are defective with replacement.