Basic Math and Pre-Algebra For Dummies (90 page)

So the probability that the coin will land heads up is
.

So what's the probability that, when you roll a die, the number 3 will land face up? To figure this one out, notice that there are
six
total outcomes (1, 2, 3, 4, 5, and 6), but in only
one
of these does 3 land face up. To find the probability of this outcome, make a fraction as follows:

So the probability that the number 3 will land face up is
.

And what's the probability that, if you pick a card at random from a deck, it'll be an ace? To figure this out, notice that there are
52
total outcomes (one for each card in the deck), but in only
4
of these do you pick an ace. So

So the probability that you'll pick an ace is
, which reduces to
(see Chapter
9
for more on reducing fractions).

 Probability is always a number from 0 to 1. When the probability of an outcome is 0, the outcome is
impossible.
When the probability of an outcome is 1, the outcome is
certain.

Although the basic probability formula isn't difficult, sometimes finding the numbers to plug into it can be tricky. One source of confusion is in counting the number of outcomes, both target and total. In this section, I focus on tossing coins.

When you flip a coin, you can generally get two total outcomes: heads or tails. When you flip two coins at the same time — say, a penny and a nickel — you can get four total outcomes:

When you flip three coins at the same time — say, a penny, a nickel, and a dime — eight outcomes are possible:

Notice the pattern: Every time you add a coin, the number of total outcomes doubles. So if you flip six coins, here's how many total outcomes you have:

The number of total outcomes equals the number of outcomes per coin (2) raised to the number of coins (6): Mathematically, you have 2
⁶
= 64.

 Here's a handy formula for calculating the number of outcomes when you're flipping, shaking, or rolling multiple coins, dice, or other objects at the same time: