CHAPTER 13.3Geometric Probability

INTRO TO PROBABILITY

Probability is the chance that something will happen.

THEORETICAL PROBABILITY

Suppose that Sowmya rolls a die. What is the probability that she will roll

a 3? What is the probability that she will roll

an even number? What is the probability that she will roll

a 4 followed by a 6?

SUPPOSE THAT YOU HAVE 10 RED, 6 BLUE, 3 GREEN AND 4 YELLOW MARBLES IN A BAG What is the probability of picking a blue

marble? What is the probability of picking a

green or yellow marble? What is the probability of picking two

red marbles in a row without replacement?

EXAMPLE 1Use Lengths to Find Geometric Probability

Point Z is chosen at random on AD. Find the probability that Z is on AB.

Answer: The probability that Z is on AB is ,

approximately 0.18, or approximately 18%.

EXAMPLE 1Point R is chosen at random on LO. Find the probability that R is on MN.

A.

B.

C.

D.

EXAMPLE 2 Model Real-World Probabilities

ORBITS Halley’s Comet orbits the earth every 76 years. What is the probability that Halley’s Comet will complete an orbit within the next decade?

EXAMPLE 2

SUBWAY You are in the underground station waiting for the next subway car, and are unsure how long ago the last one left. You do know that the subway comes every sixteen minutes. What is the probability that you will get picked up in the next 12 minutes?

A. B.

C. D.

EXAMPLE 3 Use Area to Find Geometric Probability

DARTS The targets of a dartboard are formed by 3 concentric circles. If the diameter of the center circle is 4 inches and the circles are spread 3 inches apart, what is the probability that a player will throw a dart into the center circle?

EXAMPLE 3

A. about 31%

B. about 33%

C. about 35%

D. about 37%

RING TOSS If at a carnival, you toss a ring and it lands in the red circle shown below, then you win a prize. The diameter of the circle is 4 feet. If the dimensions of the blue table are 8 feet by 5 feet, what is the probability if the ring is thrown at random that you will win a prize?

EXAMPLE 4Use Angle Measures to Find Geometric Probability

A. Use the spinner to find P(pointer landing on section 3).

Answer: The probability of landing on section 3 is approximately 34%.

EXAMPLE 4Use Angle Measures to Find Geometric Probability

B. Use the spinner to find P(pointer landing on section 1).

Answer: The probability of landing on section 1 is approximately 7%.

EXAMPLE 4A. Use the spinner to find

P(pointer landing on section C).

A. about 17%

B. about 16%

C. about 18%

D. about 27%

EXAMPLE 4B. Use the spinner to find

P(pointer landing on section E).

A. about 24%

B. about 26%

C. about 27%

D. about 38%

THE SMALLEST CIRCLE HAS A RADIUS OF 1, THE NEXT HAS A RADIUS OF 2, THE THIRD A RADIUS OF 3, AND SO ON…

P(score of exactly 100)?

P(score of exactly 20)?

P(landing in a blue section)?

P(scoring at least 30)?