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
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
If, in any event
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
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 half-dollar? c. he will not draw a quarter?