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Chapter 6: Problem 1

Define the term chance experiment, and give an example of a chance experiment with four possible outcomes.

Short Answer

Expert verified
A chance experiment, also known as a random experiment, is any process or course of action where the outcome is uncertain. An example of this would be throwing a two-sided die twice. The possible outcomes are: landing on 1, landing on 2, landing first on 1 and then on 2, landing first on 2 and then on 1.

Step by step solution

01

Provide Definition

A chance experiment, also known as a random experiment, is any process or course of action where the outcome is uncertain. It comes from the field of probability and is defined as a situation where more than one outcome is possible and we don't know which one will result.
02

Create an Example

Consider tossing a two-sided die (with sides 1, 2). Because the die is fair and every side is equally likely, there are four possible outcomes. These outcomes are: landing on 1, landing on 2, landing first on 1 and then on 2, landing first on 2 and then on 1.
03

Confirm the Outcomes are Different and All Possible Outcomes are Included

It's important to confirm that all four outcomes are different and all possible outcomes are included. In this case, each outcome is distinct and all possible results of throwing the die twice are represented.

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Most popular questions from this chapter

Suppose that a box contains 25 bulbs, of which 20 are good and the other 5 are defective. Consider randoml selecting three bulbs without replacement. Let \(E\) denote the event that the first bulb selected is good, \(F\) be the event that the second bulb is good, and \(G\) represent the event that the third bulb selected is good. a. What is \(P(E)\) ? b. What is \(P(F \mid E)\) ? c. What is \(P(G \mid E \cap F)\) ? d. What is the probability that all three selected bulbs are good?

Let \(F\) denote the event that a randomly selected registered voter in a certain city has signed a petition to recall the mayor. Also, let \(E\) denote the event that a randomly selected registered voter actually votes in the recall election. Describe the event \(E \cap F\) in words. If \(P(F)=.10\) and \(P(E \mid F)=.80\), determine \(P(E \cap F)\).

A certain company sends \(40 \%\) of its overnight mail parcels by means of express mail service \(A_{1}\). Of these parcels, \(2 \%\) arrive after the guaranteed delivery time (use \(L\) to denote the event late delivery). If a record of an overnight mailing is randomly selected from the company's files, what is the probability that the parcel went by means of \(A_{1}\) and was late?

A deck of 52 cards is mixed well, and 5 cards are dealt. a. It can be shown that (disregarding the order in which the cards are dealt) there are \(2,598,960\) possible hands, of which only 1287 are hands consisting entirely of spades. What is the probability that a hand will consist entirely of spades? What is the probability that a hand will consist entirely of a single suit? b. It can be shown that exactly 63,206 hands contain only spades and clubs, with both suits represented. What is the probability that a hand consists entirely of spades and clubs with both suits represented? c. Using the result of Part (b), what is the probability that a hand contains cards from exactly two suits?

A transmitter is sending a message using a binary code, namely, a sequence of 0's and 1's. Each transmitted bit \((0\) or 1\()\) must pass through three relays to reach the receiver. At each relay, the probability is \(.20\) that the bit sent on is different from the bit received (a reversal). Assume that the relays operate independently of one another: transmitter \(\rightarrow\) relay \(1 \rightarrow\) relay \(2 \rightarrow\) relay \(3 \rightarrow\) receiver a. If a 1 is sent from the transmitter, what is the probability that a 1 is sent on by all three relays? b. If a 1 is sent from the transmitter, what is the probability that a 1 is received by the receiver? (Hint: The eight experimental outcomes can be displayed on a tree diagram with three generations of branches, one generation for each relay.)
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