bin holds 999 fair coins and one twoheaded coin. A coin was drawn at random
from the bin. The drawn coin was tossed ten times. We do not return it to the
bin. Every time the result of the tossing is head. What is the probability
that the drawn coin is the twoheaded coin?
We introduce the random
events
These events have the
properties
We denote as
the observed sample of ten tosses. We are interested in calculation of
Prob
.
By the formula (
Inversion_remark
) we
have
Clearly,
The
Prob
may be determined from the (
Total
probability rule
)
Therefore,
