Suppose financial analyst is predicting market raise/drop, and they are of 2/3 probability correct. It means if market raise, they have 2/3 probability predict market is raise, and if market drop, they have 2/3 probability predict market is drop.
If I am asking 3 analyst (suppose they are independent), what is the probability two of them are predicting the right results? Could it be simply calculated as 2/3 * 2/3 * (1-2/3)?
Another way of thinking is, P(two predict raise, one predict drop | market raise) * P (market raise)+ P(two predict drop, one predict raise | market drop) * P (market drop).
But the latter solution is more complex and require know prior probability (P (market raise) and P (market drop)). Just wondering if the first one is correct? Thanks.
Edit 1, BTW, in my scenario, analyst are independent.