Suppose that you are managing a portfolio. Consider the experiment where you check if the portfolio...

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Suppose that you are managing a portfolio. Consider the experiment where you check if the portfolio has increased in value over the current day or not. On any given day, the probability that the portfolio increases in value is p and the probability that it does not increase in value is 1 - p. Assume that you repeat this experiment n times (over n consecutive days) and that each of these experiments are independent of the others. 3.1 Part a What is the probability that the portfolio increases in value every day? 1 3.2 Part b What is the probability that the portfolio increases in value at least once over the n days? 3.3 Part c What is the probability that the portfolio increases in value exactly k days out of the n (where 0 k n)? Suppose that you are managing a portfolio. Consider the experiment where you check if the portfolio has increased in value over the current day or not. On any given day, the probability that the portfolio increases in value is p and the probability that it does not increase in value is 1 - p. Assume that you repeat this experiment n times (over n consecutive days) and that each of these experiments are independent of the others. 3.1 Part a What is the probability that the portfolio increases in value every day? 1 3.2 Part b What is the probability that the portfolio increases in value at least once over the n days? 3.3 Part c What is the probability that the portfolio increases in value exactly k days out of the n (where 0 k n)?