"Not" means 1 minus

A path has 10 equal stones. 4 are wet and the rest are dry. You step on one stone without looking. What is the chance it is dry?

Dry stones are 6 of 10. The chance is 3/5.

The rule

P(not E) = 1 − P(E)

• Not E — every outcome that is not in E. The book calls it the complement of E.
• E and "not E" share nothing. Together they cover everything. So P(E) + P(not E) = 1.
• Elementary event — an event with just one outcome. Take all elementary events of one pick. Their chances add up to 1.

When it saves time

A spinner has 4 equal parts, numbered 1 to 4. Spin it two times. What is P(at least one 4)? At least one 4 means one 4 or two 4s.

1. All results: 4 × 4 = 16 pairs.
2. Each spin has 3 results that are not 4. So no 4 at all: 3 × 3 = 9 pairs. P(no 4) = 9/16.
3. P(at least one 4) = 1 − 9/16 = 7/16.

Check by listing all 16 pairs. 7 pairs have a 4.

Now try it. Slide the number of wet stones. Watch both chances change.

Try the lab to finish this lesson.