 4.6.40: An experiment can result in one of five equallylikely simple events...
 4.6.41: Refer to Exercise 4.40. Use the definition of acomplementary event ...
 4.6.42: Refer to Exercise 4.40. Use the definition ofconditional probabilit...
 4.6.43: Refer to Exercise 4.40. Use the Addition andMultiplication Rules to...
 4.6.44: Refer to Exercise 4.40.a. Are events A and B independent?b. Are eve...
 4.6.45: Suppose P(A) .1 and P(B) .5.a. If P(AB) .1, what is P(A B)?b. If P(...
 4.6.46: Dice An experiment consists of tossing a singledie and observing th...
 4.6.47: Refer to Exercise 4.46.a. Are events A and B independent? Mutually ...
 4.6.48: Two fair dice are tossed.a. What is the probability that the sum of...
 4.6.49: Suppose that P(A) .4 and P(B) .2. If eventsA and B are independent,...
 4.6.50: Suppose that P(A) .3 and P(B) .5. Ifevents A and B are mutually exc...
 4.6.51: Suppose that P(A) .4 and P(A B) .12.a. Find P(BA).b. Are events A a...
 4.6.52: An experiment can result in one or both ofevents A and B with the p...
 4.6.53: Refer to Exercise 4.52.a. Are events A and B mutually exclusive? Ex...
 4.6.54: 4 Drug Testing Many companies are now testingprospective employees ...
 4.6.55: Grant Funding Suppose a group of researchproposals was evaluated by...
 4.6.56: Drug Offenders A study of drug offenderswho have been treated for d...
 4.6.57: Use the probabilities of Exercise 4.56 to showthat these equalities...
 4.6.58: The Birthday people enter aroom and their birthdays (ignoring years...
 4.6.59: The Birthday Problem, continued If n peopleenter a room, find these...
 4.6.60: Starbucks or Peets? A college student frequentsone of two coffee ho...
 4.6.61: Inspection Lines A certain manufactured itemis visually inspected b...
 4.6.62: Smoking and Cancer A survey of people in agiven region showed that ...
 4.6.63: Smoke Detectors A smokedetector systemuses two devices, A and B. I...
 4.6.64: Plant Genetics In 1865, Gregor Mendel suggesteda theory of inherita...
 4.6.65: Soccer Injuries During the inaugural season ofMajor League Soccer i...
 4.6.66: Choosing a Mate Men and women often disagreeon how they think about...
 4.6.67: Kobe and Lamar Two stars of the LA Lakersare very different when it...
 4.6.68: Golfing Player A has entered a golf tournamentbut it is not certain...
Solutions for Chapter 4.6: Independence, Conditional Probability, and the Multiplication Rule
Full solutions for Introduction to Probability and Statistics 1  14th Edition
ISBN: 9781133103752
Solutions for Chapter 4.6: Independence, Conditional Probability, and the Multiplication Rule
Get Full SolutionsSince 29 problems in chapter 4.6: Independence, Conditional Probability, and the Multiplication Rule have been answered, more than 9205 students have viewed full stepbystep solutions from this chapter. This expansive textbook survival guide covers the following chapters and their solutions. This textbook survival guide was created for the textbook: Introduction to Probability and Statistics 1, edition: 14. Chapter 4.6: Independence, Conditional Probability, and the Multiplication Rule includes 29 full stepbystep solutions. Introduction to Probability and Statistics 1 was written by and is associated to the ISBN: 9781133103752.

`error (or `risk)
In hypothesis testing, an error incurred by rejecting a null hypothesis when it is actually true (also called a type I error).

aerror (or arisk)
In hypothesis testing, an error incurred by failing to reject a null hypothesis when it is actually false (also called a type II error).

Addition rule
A formula used to determine the probability of the union of two (or more) events from the probabilities of the events and their intersection(s).

Bayesâ€™ theorem
An equation for a conditional probability such as PA B (  ) in terms of the reverse conditional probability PB A (  ).

Block
In experimental design, a group of experimental units or material that is relatively homogeneous. The purpose of dividing experimental units into blocks is to produce an experimental design wherein variability within blocks is smaller than variability between blocks. This allows the factors of interest to be compared in an environment that has less variability than in an unblocked experiment.

Causeandeffect diagram
A chart used to organize the various potential causes of a problem. Also called a ishbone diagram.

Conditional probability
The probability of an event given that the random experiment produces an outcome in another event.

Conditional probability density function
The probability density function of the conditional probability distribution of a continuous random variable.

Confounding
When a factorial experiment is run in blocks and the blocks are too small to contain a complete replicate of the experiment, one can run a fraction of the replicate in each block, but this results in losing information on some effects. These effects are linked with or confounded with the blocks. In general, when two factors are varied such that their individual effects cannot be determined separately, their effects are said to be confounded.

Contour plot
A twodimensional graphic used for a bivariate probability density function that displays curves for which the probability density function is constant.

Cumulative distribution function
For a random variable X, the function of X deined as PX x ( ) ? that is used to specify the probability distribution.

Cumulative normal distribution function
The cumulative distribution of the standard normal distribution, often denoted as ?( ) x and tabulated in Appendix Table II.

Defect concentration diagram
A quality tool that graphically shows the location of defects on a part or in a process.

Defectsperunit control chart
See U chart

Designed experiment
An experiment in which the tests are planned in advance and the plans usually incorporate statistical models. See Experiment

Estimate (or point estimate)
The numerical value of a point estimator.

Factorial experiment
A type of experimental design in which every level of one factor is tested in combination with every level of another factor. In general, in a factorial experiment, all possible combinations of factor levels are tested.

Fractional factorial experiment
A type of factorial experiment in which not all possible treatment combinations are run. This is usually done to reduce the size of an experiment with several factors.

Gamma function
A function used in the probability density function of a gamma random variable that can be considered to extend factorials

Geometric random variable
A discrete random variable that is the number of Bernoulli trials until a success occurs.