PROBABILITY OF SUCCESS

If a trial must result in any of n equally likely ways, and if s is the number of successful ways and f is the number of failing ways, the probability of success is

where

EXAMPLE: What is the probability that a coin will land heads up?

SOLUTION: There is only one way the coin can land heads up; therefore, s equals 1. There is also only one way the coin can land other than heads up; therefore, f equals 1. Since

and

f=1

then the probability of success is

This, then, is the ratio of successful ways in which the trial can succeed to the total number of ways the trial can result.

EXAMPLE: What is the probability that a die (singular of dice) will land with a 3 showing on the upper face?

SOLUTION: A die has a total of 6 sides. Therefore the die can land with a 3 face up 1 favorable way and 5 unfavorable ways.

Since

s=1

and

f=5

then

EXAMPLE: What is the probability of drawing a black marble from a box of marbles if all 6 of the marbles in the box are white?

SOLUTION: There are no favorable ways of success and there are 6 total ways. Therefore,

s=0

and

f=6

so that

EXAMPLE: What is the probability of drawing a black marble from a box of 6 black marbles?

SOLUTION: There are 6 successful ways and no unsuccessful ways of drawing the marble. Therefore,

s=6

and

f=0

so that

The previous two examples are the extremes of probabilities and intuitively demonstrate that the probability of an event ranges from 0 to 1 inclusively.

EXAMPLE: A box contains 6 hard lead pencils and 12 soft lead pencils. What is the probability of drawing a soft lead pencil from the box?

SOLUTION: We are given

s=12

and

f=6

therefore,

PRACTICE PROBLEMS:

1. What is the probability of drawing an ace from a standard deck of 52 playing cards?

2. What is the probability of 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 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 draw a nickel?

b. he will draw a half-dollar? c. he will draw a quarter?

ANSWERS: