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Chapter 3: Q109SE (page 204)

Flawed Pentium computer chip.In October 1994, a flawwas discovered in the Pentium microchip installed in personalcomputers. The chip produced an incorrect result when dividing two numbers. Intel, the manufacturer of the Pentium chip, initially announced that such an error wouldoccur once in 9 billion divisions, or 鈥渙nce in every 27,000 years鈥� for a typical user; consequently, it did not immediately offer to replace the chip.

Depending on the procedure, statistical software packages (e.g., Minitab) may perform an extremely large number of divisions to produce the required output. For heavy users of the software, 1 billion divisions over a short time frame is not unusual. Will the flawed chip be a problem for a heavy Minitab user? [Note:Two months after the flaw was discovered, Intel agreed to replace all Pentium chips free of charge.]

Short Answer

Expert verified

The probability is 0.111 and it is fairly common

Step by step solution

01

Important formula

The formula for probability isP=favourableoutcomestotaloutcomes

02

Find that will the flawed chip be a problem for a heavy Minitab user.

Intel Corporationcommitted to replacing al Pentium chips free of charge two months after the error was detected. Then

P(U)=19=0.111

Therefore, the probability is 0.111 and it is fairly common.

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Most popular questions from this chapter

Male nannies. In a survey conducted by the International Nanny Association (INA) and reported on the INA Web site (www.nanny.org), 4,176 nannies were placed in a job in a given year. Only 24 of the nannies placed were men. Find the probability that a randomly selected nanny placed during the last year is a male nanny (a 鈥渕annie鈥�).

Forensic evidence in a criminal court case. In our legal system,the use of DNA as forensic evidence is often regarded as the most reliable type of evidence. However, most of the DNA code is the same for all humans. Consequently, assessing the probability of the DNA code that varies among individuals is the key to a successful case. Chance (Vol. 28, 2015) published an article on the use of DNA in a criminal case. The evidence found at the crime scene consisted of two alleles (sequences of DNA code), denoted {6/9}. One of these alleles comes from the individual鈥檚 mother and one from the individual鈥檚 father, but it is not known which allele-6 or 9-is from which parent. In forensic science, it is assumed that the two outcomes (alleles) are independent.

  1. DNA taken from the suspect resulted in a sequence of {6/9}. Given the evidence (E) comes from the suspect, find the probability of a DNA sequence of {6/9}. This probability-denotedPEHp-is used by the prosecution to support a claim of guilt.
  2. In the general population, the probability of observing an allele of 6 is 0.21 and the probability of an allele 9 is 0.14. Given the evidence (E) comes from a randomly selected person in the general population, find the probability of a DNA sequence of {6/9}. This probability-denotedPEHd-is used by the defense to support the suspect鈥檚 claim of not guilty.
  3. In a court of law, the likelihood ratioPEHp/PEHdis used to help decide the case. A ratio greater than 1 supports the prosecution, while a ratio less than 1 supports the defendant. Compute this likelihood ratio from the results in parts a and b and use it to make an inference.

Two fair dice are tossed, and the face on each die is observed.

  1. Use a tree diagram to find the 36 sample points contained in the sample space.
  2. Assign probabilities to the sample points in part a.
  3. Find the probability of each of the following events:

A = {3showing on each die}

B = {Sum of two numbers showing is}

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Profile of a sustainable farmer. Sustainable development or sustainable farming means finding ways to live and workthe Earth without jeopardizing the future. Studies wereconducted in five Midwestern states to develop a profileof a sustainable farmer. The results revealed that farmerscan be classified along a sustainability scale, dependingon whether they are likely (L) or unlikely (U) to engagein the following practices: (1) raise a broad mix of crops;(2) raise livestock; (3) use chemicals sparingly; and (4) usetechniques for regenerating the soil, such as crop rotation.

  1. List the different sets of classifications that are possible for the four practices (e.g., LUUL).
  2. Suppose you plan to interview farmers across the country to determine the frequency with which they fall into the classification sets you listed for part a. Because no information is yet available, assume initially that there is an equal chance of a farmer falling into any single classification set. Using that assumption, what is the probability that a farmer will be classified as unlikely on all four criteria (i.e., classified as a non-sustainable farmer)?
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Compute each of the following:

a.94

b. 72

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