Pearson Unit 6 Topic 15: Probability 15-4: Compound Probability Pearson Texas Geometry ©2016 Holt Geometry Texas ©2007

TEKS Focus: (13)(B) Determine probabilities based on area to solve contextual problems. (1)(A) Apply mathematics to problems arising in everyday life, society, and the workplace. (13)(C) Identify whether two events are independent and compute the probability of the two events occurring together with or without replacement.

DEFINITIONS: Independent Event TERM Definition Independent Event an event where the occurrence of the event does not affect the occurrence of another event Dependent Event an event where the occurrence of the event does affect the occurrence of another event Mutually Exclusive Event events that cannot happen at the same time Overlapping Event events that have outcomes in common Compound Event an event made up of two or more events

Example 1: Is the outcome of each trial an INDEPENDENT or DEPENDENT event? Choosing a number tile from 5 tiles and spinning a spinner Choosing one card from a deck of cards. Then, without replacing the card, picking another card. Independent event. The first event does not affect the next. Dependent event. The first card chosen does affect the possible outcomes of the second pick.

Example 2: A desk drawer contains 5 red pens, 6 blue pens, 3 black pens, 24 silver paper clips and 16 red paper clips. If you select a pen and a paper clip from the drawer without looking, what is the probability that you select a blue pen and a red paper clip?

Example 2 continued: P(A and B) = P (A)  P (B) A desk drawer contains 5 red pens, 6 blue pens, 3 black pens, 24 silver paper clips and 16 red paper clips. If you select a pen and a paper clip from the drawer without looking, what is the probability that you select a blue pen and a red paper clip? Round the final answer to the nearest tenth of a per cent. Let B = Selecting red paperclip P(B) = 16 = 2 40 5 Let A = Selecting blue pen P(A) = 6 = 3 14 7 P(A and B) = P (A)  P (B) 3  2 = 6 ≈ 0.171 ≈ 17.1% 7 5 35

Example 3: You roll a die and spin the spinner below . What is the probability that you roll a number less than 3 and the spinner lands on a vowel? Round the final answer to the nearest tenth of a per cent. Let A = roll number < 3 P(A) = 2 = 1 6 3 Let B = spinner lands on vowel P(B) = 1 4 P(A and B) = P (A)  P (B) 1  1 = 1 ≈ 0.083 ≈ 8.3% 3 4 12

Example 4: You throw two darts at the rectangular target shown below. Assuming the dart lands on the target at random, what is the probability that both darts land in the shaded region? Round the final answer to the nearest tenth of a per cent. Let A = dart in shaded region Let B = dart in shaded region P(A) = P(B) = 42 120 P(A and B) = P (A)  P (B) 42  42 = 16  16 ≈ 0.175 ≈ 17.5% 120 120 120 120

Example 5: At Madison High School, students who participate in only one sport each season are represented in the graph to the right. What is the probability that a student athlete selected at random plays volleyball or is on the swim team? P(volleyball or swim team) = P(volleyball) + P(swim team) 10% + 24% The probability that a student athlete plays volleyball or is on the swim team is 34%.

Example 6: What is the probability of rolling either an even number or a multiple of 3 when rolling a die? This is an overlapping event because the even number 6 Is also a multiple of 3. Use the formula P(A or B) = P(A) + P(B) – P(A and B) P(even # or multiple of 3) = P(even) + P(multiple of 3) - P(even and multiple of 3) 3 + 2 - 1 = 4 = 2 6 6 6 6 3