10-8 Geometric Probability

Probability

• Recall that the probability of an event is the likelihood that the event will occur.

• The theoretical probability of an event is the ratio of “favorable outcomes” to possible outcomes.– Can be expressed as a fraction, decimal, or

percent.

Geometric Probability

• In geometric probability, points on a segment or in a region of a plane represent outcomes.

• The geometric probability is a ratio that involves geometric measures such as length or area.

Probability and Length: Point S on AD is chosen at random. The probability that S is on BC is the ratio of the length of BC to the length of AD.

Using Segments to Find Probability

• Point K on ST is chosen at random. What is the probability that K lies on QR?

What is the probability that K lies on SR?

More Geometric Probability

Probability and Area: Point S in region R is chosen at random. The probability that S is in region N is the ratio of the area of region N to the area of region R.

Using Area to Find Probability

• A circle is inscribed in a square. Point Q in the square is chosen at random. What is the probability that Q lies in the shaded region?

A triangle is inscribed in a square. Point T in the square is selected at random. What is the probability that T lies in the shaded region?