Lesson 10.4 Practice a Answers

Algebra 2 10.4 WS Disjoint and Overlapping Events Events A and B are disjoint events. Find P(A or B). P(A) = 0.3, P(B) = 0.1 P(A or B) = 0.3 + 0.1 = 0.4 P(A) = 2/3, P(B) = 1/5 P(A or B) = 2/3 + 1/5 = 13/15 A board has 20 balloons on it (3 blue, 6 red, 7 green, 4 yellow). Your dart is equally likely to hit any point inside the board. If you throw the dart and pop a balloon, what is the probability that the balloon is red or blue? P(red or blue) = 6/20 + 3/20 = 9/20 You and your friend are among several candidates running for class president. You estimate that there is a 45% chance you will win and 25% chance your friend will win. What is the probability that you or your friend win the election? P(you or friend) = 0.45 + 0.25 = 0.7 = 70%   You are performing an experiment to determine how well plants grow under different light sources. Of the 30 plants in the experiment, 12 receive visible light, 15 receive ultraviolet light, and 6 receive both visible and ultraviolet light. What is the probability that a plant in the experiment receives visible or ultraviolet light? P(visible or UV) = 12/30 + 15/30 - 6/30 = 21/30   Of 162 students honored at an academic awards banquet, 48 won awards for mathematics and 78 won awards for English. There are 14 students who won awards for both mathematics and English. A newspaper chooses a student at random for an interview. What is the probability that a student interviewed won an award for English or mathematics? P(English or Math) = 48/162 + 78/162 - 14/162 = 112/162 = 56/81 ≈ 69.1%   For #7-8, you roll a six-sided die. Find P(A or B). Event A: Roll a 6 Event B: Roll a prime number (2, 3, 5) P(A or B) = 1/6 + 3/6 = 4/6 = 2/3 Event A: Roll an odd number (1, 3, 5) Event B: Roll a number less than 5 (1, 2, 3, 4) P(A or B) = 3/6 + 4/6 - 2/6 = 5/6 A group of 40 trees in a forest are not growing properly. A botanist determines that 34 of the trees have a disease or are being damaged by insects, with 18 having a disease and 20 being damaged by insects. What is the probability that a randomly selected tree has both a disease and is being damaged by insects? 34/40 = 18/40 + 20/40 - x 4/40 = x x = 1/10 or 10%   **10) A company paid overtime wages or hired temporary help during 9 months of the year.** Overtime wages were paid during 7 months, and temporary help was hired during 4 months. At the end of the year, an auditor examines the accounting records and randomly selects one month to check the payroll. What is the probability that the auditor will select a month in which the company paid overtime wages and hired   temporary help? 9/12 = 7/12 + 4/12 - x x = 2/12 = 1/6 **11) The Redbirds trail the Bluebirds by one goal with 1 minute left in the hockey game. The Redbirds' coach must decide whether to remove the goalie and add a frontline player. The probabilities of each team scoring are shown in the table.**   | | Redbirds Score | Redbirds Do Not Score | |--------|-----------------|------------------------| | Goalie | 0.1 | 0.9 | | No Goalie | 0.3 | 0.6 | a) Find the probability that the Redbirds score and the Bluebirds do not score when the coach leaves the goalie in. 0.1 * 0.9 = 0.09 or 9% b) Find the probability that the Redbirds score and the Bluebirds do not score when the coach takes the goalie out. 0.3 * 0.4 = 0.12 or 12% c) Based on parts (a) and (b), what should the coach do? **Leave the goalie in** **12) You are dealt 1 card from a 52-card deck. Find the probability that you are dealt:** a) a 7 or a red card 4/52 + 26/52 - 2/52 = 28/52 = 7/13 ≈ 53.8% b) a 5 or a black card 4/52 + 26/52 - 2/52 = 28/52 = 7/13 ≈ 53.8% c) a heart or a face card 13/52 + 12/52 - 3/52 = 22/52 = 11/26 ≈ 42.3% d) a card greater than a 2 and less than a 7 or a diamond 20/52 + 13/52 - 5/52 = 28/52 = 7/13 ≈ 53.8% **13) You randomly draw 2 marbles out of a bag containing 6 green marbles, 4 blue marbles, and 5 white marbles. Find each probability:** a) You pick a marble, put it back, and then pick another one. What is the probability both marbles will be white? 5/15 * 5/15 = 25/225 = 1/9 b) You pick a marble and keep it, then pick another marble. What is the probability the first marble will be blue and the second marble will be white? 4/15 * 5/14 = 2/21 ≈ 9.5%