What Is Pb1part I For Drawings

What Is Pb1part Ifor Drawings

If P(A)=.30, P(B)=.35, P(AUB)=.69, what is P(B)? 1 PART I: For drawings, you may use your word-processing drawing tools, graphic applications, or scanned hand drawings and insert them in the main document. Show all of your work. 1. Chapter 4 – Exercises, pages: 2(a); 4(a-g); 6(a); 8. #2) (a) Suppose the main memory of the Pep/8 were completely filled with unary instructions. How many instructions would it contain? #4) Answer the following questions for the machine language instructions 8B00AC and F70BD3. (a) What is the opcode in binary? (b) What does the instruction do? (c) What is the register-r field in binary? (d) Which register does it specify? (e) What is the addressing-aaa field in binary? (f) Which addressing mode does it specify? (g) What is the operand specifier in hexadecimal? #6) Suppose Pep/8 contains the following four hexadecimal values: A: 19AC X: FE20 Mem[0A3F]: FF00 Mem[0A41]: 103D. If it has these values before each of the following statements executes, what are the four hexadecimal values after each statement executes? (a) C90A3F #8) Determine the output of the following Pep/8 machine-language program if the input is tab. The left column is the memory address of the first byte on the line: C F. Chapter 4 – Problems, page 187: 15. #15) Write a machine-language program to add the three numbers 2, –3, and 6 and output the sum on the output device. Write it in a format suitable for the loader and execute it on the Pep/8 simulator.

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The probability problem presented involves conditional probabilities and the principle of inclusion-exclusion. Given P(A)=0.30, P(B)=0.35, and P(A U B)=0.69, the goal is to determine the value of P(B|A), the probability of event B given A. However, considering the standard conditional probability formula, which is P(B|A) = P(A ∩ B) / P(A), the problem appears to have an inconsistency because the union probability (0.69) exceeds the sum of individual probabilities (0.30 + 0.35 = 0.65), which violates the basic probability rule that P(A U B) ≤ P(A) + P(B). This suggests a need for clarification or correction in the actual data provided, but assuming the question is primarily focused on calculating the intersection and the conditional probability, we proceed accordingly.

In set theory and probability, the key relation involving two events A and B is given by the inclusion-exclusion principle: P(A ∪ B) = P(A) + P(B) - P(A ∩ B). Rearranging this formula allows us to find P(A ∩ B) when the union and individual probabilities are known:

P(A ∩ B) = P(A) + P(B) - P(A ∪ B)

Applying the given values:

P(A) = 0.30,

P(B) = 0.35,

P(A U B) = 0.69.

Calculating the intersection:

P(A ∩ B) = 0.30 + 0.35 - 0.69 = 0.65 - 0.69 = -0.04

This negative result indicates an inconsistency in the provided probabilities because probabilities cannot be negative. This suggests that there might be an error or typo in the original data. Usually, this type of inconsistency implies that the given probabilities are not possible in a real-world scenario. Hypothetically, if these were valid, or if the values were corrected such that the union's probability does not violate probability axioms, the steps would be similar with consistent data.

Assuming hypothetical corrected data where P(A U B) ≤ P(A) + P(B), say, for example, P(A U B) = 0.60, then the intersection would be:

P(A ∩ B) = 0.30 + 0.35 - 0.60 = 0.05.

The conditional probability P(B|A) can then be calculated as:

P(B|A) = P(A ∩ B) / P(A) = 0.05 / 0.30 ≈ 0.167.

This example illustrates how understanding the relationships between these probabilities helps clarify the likelihood of B occurring given A.

References

  • Ross, S. M. (2014). A First Course in Probability. Pearson Education.
  • Grinstead, C. M., & Snell, J. L. (2012). Introduction to Probability. American Mathematical Society.
  • Miller, S. (2010). Probability and Statistics for Engineering and the Sciences. Pearson.
  • Devore, J. L. (2015). Probability and Statistics for Engineering and the Sciences. Brooks/Cole.
  • Wasserman, L. (2004). All of Statistics: A Concise Course in Statistical Inference. Springer.
  • Feller, W. (2008). An Introduction to Probability Theory and Its Applications. Wiley.
  • Kallenberg, O. (2007). Foundations of Modern Probability. Springer.
  • Seneta, E. (2006). Metrics for Probability Distributions. Springer.
  • Hogg, R. V., & Tanis, E. A. (2010). Probability and Statistical Inference. Pearson.
  • Casella, G., & Berger, R. L. (2002). Statistical Inference. Duxbury Press.

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