PROBABILITY OF FAILURE
As before, if a trial results in any of n equally likely
ways, and s is the number of successful ways and f is the number of failures,
the probability of failure is
^{
}
or
where
s+f=n
or
ns=f
A trial must result in either success or failure. If
success is certain then p equals 1 and q equals
0. If success is impossible then p equals 0 and q equals
1. Combining both events, for either case, makes the probability of success
plus the probability of failure equal to 1. If
and
then
If, in any event
p+q=1
then
In the case of tossing a coin, the probability of success
is
and the probability of failure is
EXAMPLE:
What is the probability of not drawing a
black marble from a box containing 6 white, 3 red, and 2 black marbles?
SOLUTION:
The probability of drawing a black marble
from the box is
Since the probability of drawing a marble is 1, then the
probability of not drawing a black marble is
PRACTICE PROBLEMS:
Compare the following problems and answers with the
preceding problems dealing with the probability of success:
1. What is the probability of not drawing an ace from a
standard deck of 52 playing cards?
2. What is the probability of not drawing a black ace from
a standard deck of playing cards?
3. If a die is rolled, what is the probability of an odd
number not showing on the upper face?
4. A man has 3 nickels, 2 dimes, and 4 quarters in his
pocket. If he draws a single coin from his pocket, what is the probability
that
a. he will not draw a nickel?
b. he will not draw a halfdollar? c. he will not draw a quarter?
ANSWERS:
^{
}
