This question highlights many notions; thus several complications arise. In my opinion, several variables affect the validity of the answer. In simpler terms, the answer in the textbook should be one that is concurrent to the question. Therefore, to address this situation you must: firstly check that the question under the investigation and the answer upon your fore-mentioned question relates back to your chosen question, that is, (note, I will use some examples that may help you in your understanding of this post) to check the answer for Question 1, you must look up the Answer 1, your problem may be thus. If however your question does not match the answer, check that the exercise also corresponds to the exercise upon your completion. If this is not the case, fear not, there are other ways to check the validity of the question and answer.
However, I must address the notions of probability laws, by-which your answer may be affected by; The Monte Carlo fallacy, on that:
The Gambler's fallacy, also known as the Monte Carlo fallacy (because its most famous example happened in a Monte Carlo Casino in 1913),[1][2] and also referred to as the fallacy of the maturity of chances, is the belief that if deviations from expected behaviour are observed in repeated independent trials of some random process, future deviations in the opposite direction are then more likely.
thus, the aboveforementioned responses may not be right, due to the numerical influences in which they were taken, this corresponds to something known as the Bandwagon effect bywhich influences to an individual's answer may be influenced by the sheer number of other, often wrong answers. Another factor influencing the answer may be:
The proposition in probability theory known as the law of total expectation, the law of iterated expectations, Adam's law, the tower rule, the smoothing theorem, among other names, states that if X is an integrable random variable (i.e., a random variable satisfying E( | X | ) < ∞) and Y is any random variable, not necessarily integrable, on the same probability space, then
i.e., the expected value of the conditional expected value of X given Y is the same as the expected value of X.
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If, after you have read, checked (and rechecked, mind you; as you should know now that the Law of total expectations, Monte Carlo fallacy and Bandwagon effect may influence your ability to make valid calculations). You may find that the answer in your book was in fact correct therefore, following these above steps, you would of proved the textbook answers wrong, and then proceed to sue the producers for both misleading information and wasting your time.
Thank you for reading my post
