Ap Stats Chapter 14 Reading Guide Answers

Folio history last edited by Mrs. Gallagher 13 years, 11 months ago

Chapter 14: From Randomness to Probability

Key Vocabulary:

probability- long-run relative frequency.

trial- a single attempt or realization of a random phenomenon.

outcome- the event of a trial...the value measured, observed, or reported for an private instance of that trial

event- a collection of outcomes.  Usually we place events in order to attach probabilities to them.  Nosotros denote events with bold capital letters such as A, B or C

independent - The upshot of i trial doesn't influence of change the result of another.

Police of Big Numbers - states that the long-run relative frequency of repeated independent events gets closer and closer to the true relative frequency every bit the number of trials increases.

complement- the set up of outcomes that are not in an result.  The Complement Dominion states that that the risk (probability) of an upshot occuring is 1 minus the probability that does non happen.

disjoint -also chosen "mutually exclusive"--Ii events are disjoint if they share no common outcomes.

1. In statistics, what is meant by the term random?

 Something is random when we know what outcomes could happen, but non which item values did or will happen.  For instance on pages 274-275, in the example with the crimson and greenish lights, your driving is what is random.  The light was gear up on a timer, so you tin easily predict when the light will be red or green.  However you will never bulldoze at the exact same speed, at the exact same time, under the verbal aforementioned circumstances, and then your driving volition be random.

2. In statistics, what is meant by probability?

a numerical measure out of the likelihood of an upshot. Is a number from 0 to 1.

THE PROBABILITY Calibration
          +----------------------------+----------------------------+
          0                           .5                            1
          result never           result and "not consequence"             always
          will occur            result are probable                  will occur
          to occur

iii. What does information technology mean for trials to be independent?

this means that the upshot of one trial doesnt influence or modify the upshot of another.

iv. How is the Law of Big Numbers related to probability?

The Police force of Large Numbers gurantees that somewhen probabilities will settle downwardly (in the long run).  Information technology says that in the long run, relative frequencies gets closer and closer to the true frequency as we do more and more trials.  Otherwise, how could nosotros be sure that the probabilitis would just jump around forever and never settle downwards? This law is oftern misunderstood.  For example, many people believe that if you flip a fair coin and go v heads in a row, the money is "due" for a tails. This is false. The probability of getting either side is the same trial after trial. The money does not "remember." (Too, the "long run" is a long time, infinitely long to be exact.)

five. In statistics, what is an event?

    An event is a combination or collection of outcomes of trials.

half dozen. Explain why the probability of any event is a number betwixt 0 and i.

     Even if an event is very unlikely to occur, the probability can't be negative, and even if you are sure the issue will occur, the probability tin't be greater than one.

7. What is the sum of the probabilities of all possible outcomes?

The sum of the probabilities of all possible outcomes of a trial must be 1.

viii. Draw the probability that an event does not occur?

    An effect that does non occur has a probability of ane.

9. What is meant by the complement of an event?

     The opposite of the event

10. When are two events considered disjoint?

Two events are considered disjoint when they share no outcomes in common. if one issue occurs than the other issue cannot occur.

11. What is the probability of two disjoint events?

    For two disjoint events A and B, the probability that one or the other occurs is the sum of the probabilities of the two events.

12. What is the Multiplication Rule for independent events?

If A and B are independent events, and so the probability of A and B is P(A and B) = P(A) x P(B)

13. Tin disjoint events be contained?

No, disjoint events can NEVER be independent.  Once you know thta one of a pair of disjoint events has occured, the other is impossible.

14. If two events A and B are independent, what must be true most Ac and Bc?

15. What is meant past the wedlock of two or more events? Draw a diagram.

     The probability that 1 or the other occurs is the sum of the probabilities of the two events

 P(A U B)= P(A) + P(B), provided that A and B are disjoint.

16. State the add-on dominion for disjoint events.

If A and B are disjoint events, and then the probability of A or B is P(A or B) = P(A) + P(B)

17. What is meant past the intersection of two or more events? Depict a diagram.

The intersection of ii events means that two events happen at the same time. Ex: Sombody tin can exist a student in Depew High School and a SENIOR.  If the Venn Diagram beneath was green=student and purple=SENIOR the black=both or the intersection of the 2 events.

xviii. Explicate the difference between the union and the intersection of two or more events.

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Source: http://mrsgallagher.pbworks.com/w/page/21762568/AP%20Stats%20-%20Chapter%2014

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