 # Quant Question

There is a 50 percent chance that the Fed will cut interest rates tomorrow. On any given day, there is a 67 percent chance the DJIA will increase. On days the Fed cuts interest rates, the probability the DJIA will go up is 90 percent. What is the probability that tomorrow the Fed will cut interest rates or the DJIA will go up? A) 1.00. B) 0.72. C) 0.33. D) 0.95. Can someone help? I feel so dumb!

there are 4 possible outcomes: (cut, not cut) x (rise, fall). Can you assign the likelihoods to the 4 states (so that they add to 1)? Then the question asks you to sum up the likelihoods of 3 of the states. (Or 1 minus the likelihood of the other state.)

Would you mind placing the steps to the solution. Did you take December exam? How big of a factor is quant? Personally that is the problem child for me, I struggle with it.

B) 0.72 Given: P(I)= 0.50 P(D)=0.67 P(D|I)=0.90 P(D or I) = P(D)+P(I)-P(DI) P(DI)=P(D|I)+P(I) = 0.90 * 0.50 = 0.45 therefore P(D or I) = 0.67 * 0.50 - 0.45 P(D or I) = 0.72

KHJ these profitably questions can be a pain at first. In reality though you need to memorize the two formulas for the Addition rule and the Multiplication rule. The rest is plug and chug for most questions. From what I’ve observed this question is the typical cookie cutter question asked, in other words it appear this question is typically asked just in some other format of percentages and word problem. Sit down and read the section then immediately follow up with 5-6 of these probably questions to get the steps down and you’ll be moving in the right direction. Multiplication Rule: P(AB) = P(A|B)*P(B) the probability even A will occur given event B has occurred. Addition Rule: P(A or B) = P(A) + P(B) - P(AB) the probability that either event A or B occurs alone and not together.

check that… probability questions not “profitability questions”… need to take a break

probability of cut + probability of increase - probability of increase given cut 0.5 + 0.67 - (0.5*(0.9)) = 0.72 if i still remember this correctly…

Think of the Venn Diagram when dealing with probability questions. It allows you to picture the scenario. Circle 1 is the probability that the Fed cuts rates, which we’ll call P(F) = 0.5 or 50% Circle 2 is the probability that the Dow rises, which we’ll call P(D) = 0.67 or 67% Now, we’re told that when the Fed cuts rates, the probability of the Dow increasing is 90%. In other words, given that the Fed cut rates, the probability of the Dow rising is 90%, or P(D|F) = 0.90 What this indicates is that these are not mutually exclusive events. The probability of F or D (the key word is “or,” which translates to union in set mathematics) is the probability of F, plus the probability of D, less the overlap between the two probabilities (the intersection, or P(F and D) P(F or D) = P(F) + P(D) - P(F and D) Solving for the third component, P(F and D) = P(D|F) x P(F) P(F and D) = 0.90 x 0.50 P(F and D) = 0.45 Hence, P(F or D) = 0.5 + 0.67 - 0.45 P(F or D) = 0.72 The answer is B