Page 245 - Statistics II for Dummies

Chapter 13: Forming Associations with Two-Way Tables 229

✓ The conditional probability that a female uses a cellphone for personal
calls is .
✓ The conditional probability that a female doesn’t use a cellphone for
personal calls is .

To interpret these results, you say that within this sample, if you’re male,
you’re more likely than not to use your cellphone for personal calls (64
percent compared to 36 percent). However, the percentage of personal-call
makers is higher for females (84 percent versus 16 percent).
Notice that for the males in the previous example, the two conditional prob-
abilities (0.64 and 0.36) add up to 1.00. This is no coincidence. The males have
been broken down by cellphone use for personal calls, and because everyone
in the study is a cellphone user, each male has to be classified into one group
or the other. Similarly, the two conditional probabilities for the females sum to
1.00.

Notation for conditional probabilities
You denote conditional probabilities with a straight vertical line that lists and
separates the event that’s known to have happened (what’s given) and the
event for which you want to find the probability. You can write the notation
like this: P(XX|XX). You place the given event to the right of the line and the
event for which you want to find the probability to the left of the line. For
example, suppose you know someone is female (F) and you want to find out
the chance she’s a Democrat (D). In this case, you’re looking for P(D|F). On
the other hand, say you know a person is a Democrat and you want the prob-
ability that person is female — you’re looking for P(F|D).

The vertical line in the conditional probability notation isn’t a division sign; it’s just
a line separating events A and B. Also, be careful of the order in which you place A
and B into the conditional probability notation. In general, P(A|B) ≠ P(B|A).

Following is the notation used for the conditional probabilities in the cell-
phone example:

✓ P(Yes|M) = 0.64. You can say it this way: “The probability of Yes given
Male is 0.64.”
✓ P(No|M) = 0.36. In human terms, say, “The probability of No given Male
is 0.36.”
✓ P(Yes|F) = 0.84. Say this one with gusto: “The probability of Yes given
Female is 0.84.”
✓ P(No|F) = 0.16. You translate this notation by saying, “The probability of
No given Female is 0.16.”

20_466469-ch13.indd 229 7/24/09 9:47:58 AM