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Chapter 4: Problem 1

Define the following terms: experiment, outcome, sample space, simple event, and compound event.

Short Answer

Expert verified
An 'experiment' is a procedure that yields an observable result, an 'outcome' is the result obtained, the 'sample space' is the set of all possible outcomes, a 'simple event' is an event with one outcome in the sample space, and a 'compound event' consists of more than one simple event.

Step by step solution

01

Define Experiment

An experiment in probability is any procedure or action that results in an observable outcome. Examples could be rolling a dice, flipping a coin or drawing a card from a deck.
02

Define Outcome

The outcome is the result that you get from performing the experiment. If the experiment is flipping a coin, the possible outcomes are 'head' or 'tail'.
03

Define Sample Space

The sample space, often denoted by \( S \), is the set of all possible outcomes for an experiment. If the experiment is rolling a six-sided die, the sample space would be \( S = \{1, 2, 3, 4, 5, 6\} \).
04

Define Simple Event

A simple event is an event where the outcome is a single point in the sample space. If the experiment is rolling a die, and the event is the die showing 4, then it's a simple event because only one outcome (4) satisfies this event.
05

Define Compound Event

A compound event consists of two or more simple events. It can occur in several ways. If the experiment is flipping two coins, a compound event could be both coins landing on 'head'.

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Most popular questions from this chapter

Five hundred employees were selected from a city's large private companies and asked whether or not they have any retirement benefits provided by their companies. Based on this information, the following two-way classification table was prepared. $$ \begin{array}{lcc} &{\text { Have Retirement Benefits }} \\ \hline { 2 - 3 } & \text { Yes } & \text { No } \\ \hline \text { Men } & 225 & 75 \\ \text { Women } & 150 & 50 \\ \hline \end{array} $$ a. Suppose one employee is selected at random from these 500 employees. Find the following probabilities. i. Probability of the intersection of events "woman" and "yes" ii. Probability of the intersection of events "no" and "man" b. Mention what other joint probabilities you can calculate for this table and then find them. You may draw a tree diagram to find these probabilities.

Determine the value of each of the following using the appropriate formula. $$ \begin{array}{llllllllll} 3 ! & (9-3) ! & 9 ! & (14-12) ! & { }_{5} C_{3} & { }_{7} C_{4} & { }_{9} C_{3} & { }_{4} C_{0} & { }_{3} C_{3} & { }_{6} P_{2} & { }_{8} P_{4} \end{array} $$

The probability that a student graduating from Suburban State University has student loans to pay off after graduation is .60. The probability that a student graduating from this university has student loans to pay off after graduation and is a male is \(.24\). Find the conditional probability that a randomly selected student from this university is a male given that this student has student loans to pay off after graduation.

How is the multiplication rule of probability for two dependent events different from the rule for two independent events?

A production system has two production lines; each production line performs a two-part process, and each process is completed by a different machine. Thus, there are four machines, which we can identify as two first-level machines and two second-level machines. Each of the first-level machines works properly \(98 \%\) of the time, and each of the second-level machines works properly \(96 \%\) of the time. All four machines are independent in regard to working properly or breaking down. Two products enter this production system, one in each production line. a. Find the probability that both products successfully complete the two-part process (i.e., all four machines are working properly). b. Find the probability that neither product successfully completes the two- part process (i.e., at least one of the machines in each production line is not working properly).
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