Statistics for Decision- Making in Business - Maricopa Community ...

This is definitely a small probability, but it is not the only way in which this can happen. The tail
can occur first, second, third, fourth, etc., with heads all around it. Another one would be:
The probability of this sequence is the same: 9 heads, 1 tail. This is okay, since the probability of
tossing a certain sequence does not affect the probability of getting a head or tail on the next toss.
So,
( ) ( ) ( ) ( ) ( ) ( )
Not surprisingly, there are 8 more places for the tail to have appeared. We‟ll summarize in the
table below:
Arrangement of 9 , 1
Probability
( ) ( )
( ) ( )
( ) ( )
( ) ( )
( ) ( )
( ) ( )
( ) ( )
( ) ( )
( ) ( )
( ) ( )
Since these are 10 distinct ways of getting this outcome, each with probability 0.000977 (that is,
each takes up 0.0977% of the entire sample space), the probability of getting 9 heads and 1 tail
is:
( )
As suspected, this particular event is not very likely.
What if we complicated the problem a little more and asked, what would be the probability of
having two tails mixed up in 10 total tosses
This gets more complicated, since the two tosses could occur one after another, two tosses apart,
three tosses apart, etc. To simplify our lives, it can be shown that the total number of ways in
which a binary “success” can occur is by finding the following combination:
. /
Statistics for Decision-Making in Business © Milos Podmanik Page 148