4.4. THE ABSOLUTE EXCESS OF HEADS OVER TAILS 151
4.4 Probability ofsexcess heads in 500 tosses
Illustration 2
What is the probability that there is “about the same number of heads as
tails” in 500 tosses? Here we interpret “about the same” as within 5, that is,
an absolute difference of 1% or less of the number of tosses. Note that since
500 is even, so the difference in the number of heads and tails cannot be an
odd number, so must be either 0, 2 or 4.
P[|S 500 |<5]≈P
[
|Z|≤ 5. 5 /
√
500
]
= 0. 1943
so it would be somewhat unusual (in that it occurs in less than 20% of games)
to have the number of heads and tails so close.
Illustration 3
Suppose you closely follow a stock recommendation source whose methods
are based on technical analysis. You accept every bit of advice from this
source about trading stocks. You choose 10 stocks to buy, sell or hold every
day based on the recommendations. Each day for each stock you will gain
or lose money based on the advice. Note that it is possible to gain money
even if the advice says the stocks will decrease in value, say by short-selling
or using put options. How good can this strategy be? We will make this