A stockbroker predicts whether a stock will go up or down by tossing a coin and so has a 50% chance of making a correct prediction. Another broker, who is skilled, has a 60% chance of making a correct prediction. You don’t know which broker is which, so you watch their predictions for three days. Each broker gets all three predictions correct. What are the relevant probabilities? How do you decide who is the skilled broker? Search entries or author

A skilled  broker will be right at  60% of time compared to 50%

Explanation:

Solution

Given that:

Now,

Let X  be represented as = number of correct predictions/outcomes

X foll binomial distribution with n = 3 and p = 0.5 for broker who use a toss coin

Thus,

P(X = 3) = p^3 = 0.5^3 which gives us  = 0.125

So,

For a skilled broker, Y goes with the binomial distribution with n = 3 and p is = 0.6

Then,

P(Y = 3) = 0.6^3 = 0.216

We can therefore conclude who is skilled broker by making large number of observations

Hence, we say that a skilled broker will be correct 60% of time compared to 50% .