====================================================== Fundamentals of Probability Consider the experiment of rolling two dice: one 6-sided and one 20-sided. 1. How many possible outcomes are there for this experiment? 2. Find the probabilities of each of the following events. (a) Rolling a 6 on the 6-sided die (b) NOT rolling a 6 on the 6-sided die (c) Rolling a 20 on the 20-sided die (d) NOT rolling a 20 on the 20-sided die (e) Rolling a 6 on the 6-sided die AND a 20 on the 20-sided die (f) NOT rolling a 6 on the 6-sided die AND NOT rolling a 20 on the 20-sided die. (g) Rolling a 6 on the 6-sided die OR rolling a 20 on the 20-sided die (h) Rolling a 5 on the 6-sided die (i) Rolling a 5 OR a 6 on the 6-sided die (j) Rolling an even number on the 6-sided die. 3. Using the examples from #2 as a guide, answer the following. For each question, illustrate with an example from the experiment above. (a) Finish the sentence: the probability that an event doesn't occur is... (b) Finish the sentence: if events A and B are independent (i.e. one event occurring or not occurring doesn't affect the probability that the other will occur), then the probability that both A and B occur is... (c) What is the relationship between parts (f) and (g) in #2? Can you explain why this happens? (d) Finish the sentence: if events A and B are independent, then the probability that either A or B occurs is... (e) Suppose that if you know event A happens, then you automatically know event B happened. Then what is the relationship between the probabilities of the two events? (f) Finish the sentence: if events A and B are mutually exclusive (i.e. if A occurs, B cannor occur, and vice versa), then the probability that both A and B occur is... and the probability that either A or B occurs is... 4. Imagine that throwing a dart at a dart board (a circle with radius 12 inches) is a completely uniformly distributed experiment, i.e. every point on the dart board has an equal chance at being chosen. We will treat the dart board as something we can zoom in on as close as we want, so there is no limit to how close two different points on the dart board can be to each other. (a) If the bullseye is a circle in the center with a radius of .5 inces, what is the probability the dart will land in the bullseye? (b) Pick a specific point on the dart board. What is the probability of hitting that exact point with the dart? What is the probability of not hitting that point? (c) If an event can never occur, the probability is 0, but if the probability of an event is 0, what does that mean? (d) If an event always occurs, the probability is 1, but if the probability of an event is 1, what does that mean?
【在 l***o 的大作中提到】 : 月光的概率基本功也够呛。。。扯到什么骰子6面了 :——)
m*t
18 楼
======================================= Basic Concepts Author(s) David M. Lane Prerequisites Introduction to Probability Learning Objectives Compute probability in a situation where there are equally-likely outcomes Apply concepts to cards and dice Compute the probability of two independent events both occurring Compute the probability of either of two independent events occurring Do problems that involve conditional probabilities Compute the probability that in a room of N people, at least two share a birthday Describe the gambler's fallacy Probability of a Single Event If you roll a six-sided die, there are six possible outcomes, and each of these outcomes is equally likely. A six is as likely to come up as a three, and likewise for the other four sides of the die. What, then, is the probability that a one will come up? Since there are six possible outcomes, the probability is 1/6. What is the probability that either a one or a six will come up? The two outcomes about which we are concerned (a one or a six coming up) are called favorable outcomes. Given that all outcomes are equally likely, we can compute the probability of a one or a six using the formula:
【在 l***o 的大作中提到】 : 月光的概率基本功也够呛。。。扯到什么骰子6面了 :——)
l*o
19 楼
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【在 m********t 的大作中提到】 : : ======================================= : Basic Concepts : Author(s) : David M. Lane : Prerequisites : Introduction to Probability : Learning Objectives : Compute probability in a situation where there are equally-likely outcomes : Apply concepts to cards and dice