Question

There is a 50% chance that the Fed will cut interest rates tomorrow. On any given day, there is a 67% chance the DJIA will increase. On days the Fed cuts interest rates, the probability the DJIA will go up is 90%. What is the probability that tomorrow the Fed will cut interest rates or the DJIA will go up?

1) 0.33

2) 0.95

3) 0.72

Answer 1

3) 0.72

Explanation:

The probability that tomorrow the Fed will cut interest rates (P(F)) OR the DJIA will go up (P(D)), is the sum of each event's individual probability minus their joint probability (Fed cutting interest rates AND the DJIA will going up, P(FD))

`P(F+D) = P(F) +P(D) - P(FD)\\P(F+D) = 0.5 + 0.67 - (0.5*0.9)\\P(F+D) = 0.72`

The probability that tomorrow the Fed will cut interest rates or the DJIA will go up is 0.72.