### Sample Space and Event Definition in Probability**Sample Space:**The sample space of an experiment consists of the following outcomes:\[ S = \{1, 5, 7\} \]**Defined Events:**- **X**: The outcome of the experiment is an even number- **Y**: \(\{1, 5\}\)- **Z**: \(\{1, 7\}\)**Given Information:**- **X, Y, and Z** are independent events- \( P(Y \cup Z) = \frac{1}{2} \)- Probabilities of all numbered outcomes are equal: \[ P(1) = P(5) = P(7) \]**Tasks:**A. **Venn Diagram:**Draw a Venn Diagram to represent events X, Y, Z, and all outcomes in the sample space \( S \). If an event does not exist, it can be placed outside of \( S \) or not included—this implies nonexistent events have zero likelihood.B. **Numerical Calculation:**Compute the numerical value of \( P(X \cup Y \cup Z) \).**Hint**: Use the formula for a triple union:\[P(X \cup Y \cup Z) = P(X) + P(Y) + P(Z) - P(X \cap Y) - P(X \cap Z) - P(Y \cap Z) + P(X \cap Y \cap Z)\]

The sample space of an experiment consists of the following outcomes: S = {1, 5, 7} The following…

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MATLAB: An Introduction with Applications

6th Edition

ISBN:9781119256830

Author:Amos Gilat

Publisher:Amos Gilat

Chapter1: Starting With Matlab

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Have you ever re-gifted? According to Webster's dictionary 're-gift is to give a gift you received to someone else. Suppose you take a random sample of 1000 adults and get the following results: Yes - Regifted No - Regifted Total 400 Female Male Total 160 240 400 240 360 600 600 1000 Which of the following statements is true? Select one: O The events Regift and Female are dependent because P(Regift) = P(Regift|Female). O The events Regift and Female are independent because P(Regift) = P(Regift|Female). %3! O The events Regift and Female are dependent because P(Regift) + P(Regift Female). O The events Regift and Female are independent because P(Regift) + P(Regift|Female).
7. If an experiment the events A and B can both occur then a. P(A U B) = P(A)P(B|A) b. P(A N B) = P(A)P(A|B) c. P(AN B) = P(A)P(B|A) d. P(A U B) = P(B)P(B|A) %3D
Let A, B and C be events from a common sample space such that: P(A) = 0.72, P(B) = 0.56, P(C) =0.25, P(ANB) = 0.42. P(ANC) = 0.18, P(BOC) =0 %3D Compute P(AUBUC).
1. In the experiment of tossing 3 coins, what is the probability of getting 3 heads? 2. The events x and y are mutually exclusive events. If P(x) = 0.4 and P(y) = 0.3, what is the probability of either x or y? What is the probability that neither x nor y will occur? %3D %3D 3. A student enrolled two math subjects: statistics and algebra. His chance of passing the statistics subject 0.65. His chance of passing algebra is 0.80 and his chance of passing both subjects is 0.50. What is the probability of passing at least one subject?
Suppose we have a sample with five equally likely experimental outcomes: E1, E2, E3, E4, E5 Let: A = (E1, E3, E4, E5) B= (E1, E3} C = (E2, E3, E4,) a) There are 3 methods of assigning probabilities - classical, subjective and relative frequency. Which method is used above? b) Find P(A), P(B) and P(C) c) Find A and P(AG) d) Find P(B U C^C) e) Are A and C mutually exclusive? Explain.
c) Three coin are tossed. Write down the sample space hence copy and complete the table of probabilities distribution P(X = x) of X = 0, 1, 2, and 3 heads below hence find the expected value E(X) x p(x) 0 1338 8 2 3
2.33
Given P(A and B) = 0.30, P(A) = 0.93, and P(B) = 0.32 are events A and B independent or dependent? Question 7 options: 1) Dependent 2) Independent
Let S = {E1, E2, E3, E4} be the sample space of an experiment and let = {E1, E2}, B = {E3}, and C = {E3,E4} be events from S. The probabilities of the sample points are assigned as follows: P(E1) = 0.40, P(E2) = 0.40, P(E3) = 0.10, and P(E4) = 0.10. Find P(A). %3D Select one: O a. 0.60 O b. 0.80 O C. 0.70 O d. 0.30
Let 2 = {1,2, 3, 4, 5} be the sample space of a random experiment. Let also the events A = {1,2} and B = {2, 3, 4} be such that P(A N B) = 0.1, P(A) = 0.3 and P(B) = 0.8. Find the probabilities: (a) P({2}). (b) P({1}). (c) P(A°|B), (where Aº is the complement of A).

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