HUH?? 1/64 Probability

Annotation category:
Chapter 4

Note:

The number of ways to predict the outcome of one event is 2 (either the stock goes up or down.) The probability of predicting correctly is 1/2 (since one of the two choices is correct.)

The number of ways to predict the outcome of the second event is also 2.

The number of ways to predict both events is the product of the two individual probabilities:
2 x 2 = 4. To better understand this rule, let's talk through the scenario step-by-step. For event 1, you predict either option u (stock goes up) or d (down). For event 2, you have the same two choices. Here are the possible combinations of predicting:

Event           1       2
Outcome 1       u       u
        2       u       d
        3       d       u
        4       d       d

Now if you include a third independent event with the same two possible outcomes, the number of ways of predicting all three becomes
2 x 2 x 2 = 8:

Event           1       2       3
Outcome 1       u       u       u
        2       u       u       d
        3       u       d       u
        4       u       d       d
        5       d       u       u
        6       d       u       d
        7       d       d       u
        8       d       d       d

Following this pattern, the number of ways to predict outcomes for the 6 predicted stock changes is:
2 x 2 x 2 x 2 x 2 x 2 = 64. And the number of ways of predicting all 6 correctly is just 1. Thus, the chance of predicting all 6 outcomes correctly, based purely on chance, is 1/64. If you started off with 4000 people, after 6 cycles of throwing away half, you'll end up with
4000/64 = 62... 62 very impressed people eager to pay you for more "advice"!