Statistics: Probability of Simple Events

Probability of Simple Events

Example 1: What is the probability of simultaneously flipping three coins—a penny, a nickel, and a dime—and having all three land heads?

Using the classic theory, determine the ratio of number of favorable outcomes to the number of total outcomes. Table 1 lists all possible outcomes.

TABLE 1

Possible Outcomes of Penny, Nickel, and Dime Flipping

*Outcome #*	*Penny*	*Nickel*	*Dime*
1	H	H	H
2	H	H	T
3	H	T	H
4	H	T	T
5	T	H	H
6	T	H	T
7	T	T	H
8	T	T	T

There are 8 different outcomes, only one of which is favorable (outcome #1: all three coins landing heads); therefore, the probability of three coins landing heads is 1/8, or .125.

What is the probability of exactly two of the three coins landing heads? Again, there are the 8 total outcomes, but in this case only 3 favorable outcomes (outcomes #2, #3, and #5); thus, the probability of exactly two of three coins landing heads is 3/8 or .375.

Each of the three coins being flipped in the preceding example is what is known as an independent event. Independent events are defined as outcomes that are not affected by other outcomes. In other words, the flip of the penny does not affect the flip of the nickel, and vice versa.