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48. (A) P(NOR) (B) P(S)

48. (A) P(NOR) (B) P(S)

Advanced Engineering Mathematics
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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**Transcription for Educational Website** --- **Problem Analysis and Probability Calculation** **1. Event Definitions and Tasks** (A) Find \( P(F | E) \). (B) Test events \( E \) and \( F \) for independence. **46. Problem 46** Repeat Problem 45 with the following events: - \( E \): Pointer lands on an odd number. - \( F \): Pointer lands on a prime number. Compute the indicated probabilities in Problems 47 and 48 by referring to the probability tree given below. **Probability Tree Diagram:** The tree starts with a single node labeled "Start" branching into two paths: 1. Branch leading to M: - Probability of branching: 0.3 - Subsequent branch: - M to R with probability 0.2 2. Branch leading to N: - Probability of branching: 0.7 - Two subsequent branches: - N to S with probability 0.8 - N to R with probability 0.6 **Given Problems:** **47. Calculate the following probabilities:** (A) \( P(M \cap S) \) (B) \( P(R) \) **48. Calculate the following probabilities:** (A) \( P(N \cap R) \) (B) \( P(S) \) **49. Coin Toss Scenario:** A fair coin is tossed twice. Consider the sample space: \( S = \{ HH, HT, TH, TT \} \) The events of interest are: - \( E_1 \): A head on the first toss. - \( E_2 \): A tail on the first toss. - \( E_3 \): A tail on the second toss. - \( E_4 \): A head on the second toss. For each pair of events, discuss whether they are independent and whether they are mutually exclusive. (A) \( E_1 \) and \( E_4 \) (B) \( E_1 \) and \( E_2 \) --- This transcription offers a structured approach to understanding different probability problems using a given probability tree and analyzing outcomes from a simple two-toss experiment.
Transcribed Image Text:**Transcription for Educational Website** --- **Problem Analysis and Probability Calculation** **1. Event Definitions and Tasks** (A) Find \( P(F | E) \). (B) Test events \( E \) and \( F \) for independence. **46. Problem 46** Repeat Problem 45 with the following events: - \( E \): Pointer lands on an odd number. - \( F \): Pointer lands on a prime number. Compute the indicated probabilities in Problems 47 and 48 by referring to the probability tree given below. **Probability Tree Diagram:** The tree starts with a single node labeled "Start" branching into two paths: 1. Branch leading to M: - Probability of branching: 0.3 - Subsequent branch: - M to R with probability 0.2 2. Branch leading to N: - Probability of branching: 0.7 - Two subsequent branches: - N to S with probability 0.8 - N to R with probability 0.6 **Given Problems:** **47. Calculate the following probabilities:** (A) \( P(M \cap S) \) (B) \( P(R) \) **48. Calculate the following probabilities:** (A) \( P(N \cap R) \) (B) \( P(S) \) **49. Coin Toss Scenario:** A fair coin is tossed twice. Consider the sample space: \( S = \{ HH, HT, TH, TT \} \) The events of interest are: - \( E_1 \): A head on the first toss. - \( E_2 \): A tail on the first toss. - \( E_3 \): A tail on the second toss. - \( E_4 \): A head on the second toss. For each pair of events, discuss whether they are independent and whether they are mutually exclusive. (A) \( E_1 \) and \( E_4 \) (B) \( E_1 \) and \( E_2 \) --- This transcription offers a structured approach to understanding different probability problems using a given probability tree and analyzing outcomes from a simple two-toss experiment.
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