Over Lesson 13–2 A.A B.B C.C D.D 5-Minute Check 1 From the 15 members of the prom committee, two will be chosen as chairman and treasurer. What is the probability that Julia and her friend Marco will be randomly selected as chairman and treasurer in that order?

Over Lesson 13–2 A.A B.B C.C D.D 5-Minute Check 2 A gym class is separated into teams of 8 students. Each team then randomly assigns the positions of captain and scorekeeper. What is the probability that Tina and Frank are selected for either position on their team?

Over Lesson 13–2 A.A B.B C.C D.D 5-Minute Check 3 Rico is choosing a password for his bank account from the letters of his last name: H-E-R-R-E-R-A. If he selects from the letters at random, what is the probability that the password will be his last name (Herrera)?

Over Lesson 13–2 A.A B.B C.C D.D 5-Minute Check 4 Mrs. Henderson is choosing groups of 3 students from her math class of 24 students. If the groups are randomly chosen, what is the probability that Jacob, Terrence, and Todd are in a group?

Then/Now Find probabilities by using length. Find probabilities by using area.

Concept

Substitution Example 1 Use Lengths to Find Geometric Probability Point Z is chosen at random on AD. Find the probability that Z is on AB. Length probability ratio Answer:The probability that Z is on AB is, approximately 0.18, or approximately 18%.

A.A B.B C.C D.D Example 1 Point R is chosen at random on LO. Find the probability that R is on MN.

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? We can use a number line to model this situation. Since the comet orbits every 76 years, it will orbit again in 76 years or less. On the number line below, the event of an orbit in the next 10 years is modeled by EF.

Example 2 Model Real-World Probabilities Find the probability of this event. Length probability ratio EF = 10 and EG = 76 Simplify. Answer:, approximately 0.13, or approximately 13%

A.A B.B C.C D.D 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?

Concept

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? You need to find the ratio of the area of the center circle to the area of the entire dartboard. The radius of the center circle is 4 ÷ 2 or 2 inches, while the radius of the dartboard is or 8 inches.

Example 3 Use Area to Find Geometric Probability Area probability ratio A = π r 2 Simplify. Answer:The probability that the dart hits in the center circle is or about 6%.

A.A B.B C.C D.D Example 3 about 31% 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 4 Use Angle Measures to Find Geometric Probability A.Use the spinner to find P(pointer landing on section 3). The angle measure of section 3 is 122°. Answer:The probability of landing on section 3 is approximately 34%. P(pointer landing on section 3) =

Example 4 Use Angle Measures to Find Geometric Probability B.Use the spinner to find P(pointer landing on section 1). The angle measure of section 1 is 26°. Answer:The probability of landing on section 1 is approximately 7%. P(pointer landing on section 1) =

A.A B.B C.C D.D Example 4 A.Use the spinner to find P(pointer landing on section C).

A.A B.B C.C D.D Example 4 B.Use the spinner to find P(pointer landing on section E).