# Geometric Probability Probability Recall that the probability of

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 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?

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