Algebra 2 Honors Addition Rule In its monthly report, the local animal s

Algebra 2 Honors Addition Rule In its monthly report, the local animal shelter states that it currently has 28 dogs and 16 cats available for adoption. Eight of the dogs and 6 of the cats are male. Find each of the probabilities if an animal is selected at random. Male Female Total Cats 16 Dogs 28 Total 1. P(male) 2. P(cat) 3. P(not male) 4. P(male or cat) 5. P(dog or female) 1000 students were asked “Do you ride the bus to school?” Here are the results. 10th grade 11th grade 12th grade Total Yes 370 180 85 635 No 110 133 122 365 Total 480 313 207 1000 Find the probability of randomly selecting a 6. senior who does NOT ride the bus 7. junior or senior who rides the bus 8. student who rides the bus or is a sophomore 9. student who does not ride the bus or is a senior 10. student who is a junior or who rides the bus A student is holding 10 cards numbered 1 – 10. Find the probability of selecting a 11. even number or a number greater than 8 12. odd number or a number less than 5 13. multiple of 2 or a multiple of 3 14. a multiple of 5 or a multiple of 6 15. a multiple of 8 or a number less than 5 Algebra 2 Honors -­‐Conditional Probability Joel surveyed his classmates and asked “Do you like school?” The results are as follows: Liked Disliked No opinion Total Male 12 5 2 19 Female 10 3 1 14 Total 22 8 3 33 Find the probability of randomly selecting a classmate who 1) likes school 2) is not a female 3) likes school, given they are female 4) is a male, given they do not like school 5) is a female, given they like school 6) has no opinion, given they are female 7) does not like school, given they are female 8) likes school, given they are male The question, "Do you smoke?" was asked of 100 people. Results are shown in the table. Yes Not .......... Male 19 41 Female 12 28 What is the probability of a randomly selected individual (Use the table to answer #9-­‐18.) 9) a male? 10) a male and smokes? 11) a female, given that the individual smokes? 12) a smoker, given that they are female? 13) not a smoker, given that they are male? 14) P(Yes | male ) 15) P( male | yes) 16)P(no | female) 17) P( female | no ) 18) P(female and smokes) 19. Andrea is a very good student. The probability that she studies and passes her mathematics test is 17
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. If the probability that Andrea studies is , find the probability that Andrea passes her 20
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mathematics test, given that she has studied. 20. The probability that Janice smokes is 3 . The probability that she Smokes and develops lung 10
cancer is 4 . Find the probability that Janice develops lung cancer, given that she smokes. 15
21. The probability that Sue will go to Mexico in the winter and to France in the summer is 0.40 . The probability that she will go to Mexico in the winter is 0.60 . Find the probability that she will go to France this summer, given that she just returned from her winter vacation in Mexico. 22. A die is tossed. Find P(less than 5 | even) . 23. A number is selected randomly from a container containing all the integers from 10 to 50 . Find: a) P(even | greater than 40) b) P( greater than 40 | even) c) P( prime | between 20 and 40) Algebra 2 Honors Name______________________________________ Independent/Dependent Probability Period______Date_________________________ Are these events independent or dependent? Explain. 1. Rolling a red die and a green die. 2. Selecting a red card from a deck of cards, replacing it, and then selecting another red card. 3. Taking a five question true/false quiz and guessing at each question. 4. Tossing a coin and then rolling a die. 5. Selecting two cards from a deck of cards without replacing the first one before drawing the second. A coin is tossed, then a die is rolled. Find the probability of each outcome. 6. heads and a 6 7. heads and a number less than 5 8. tails and a 5 9. tails and an odd number 10. tails and a number that is a multiple of 3 11. tails and a 2 or a 3 12. heads and a number greater than 2 A bag contains 3 red and 4 white marbles. A second bag contains 6 yellow and 3 green marbles. One marble is selected from each bag. Find the probability of each outcome. 13. a red and a yellow 14. a red and a green 15. a white and a green 16. a white and a yellow In a bag there are 3 red marbles, 2 white marbles, and 4 blue marbles. Find the probability of selecting 17. a red marble and then a white marble (with replacement) 18. 2 blue marbles in a row (with replacement) 19. a white marble and then a blue marble (with replacement) 20. 2 white marbles in a row (with replacement) 21. 3 red marbles in a row (with replacement) 22. a red marble and then a white marble (without replacement) 23. 2 blue marbles in a row (without replacement) 24. a white marble and then a blue marble (without replacement) 25. 2 white marbles in a row (without replacement) 26. 3 red marbles in a row (without replacement) Addition Rule 2
1. Are these events mutually exclusive or inclusive?
a. Event A: randomly selecting a junior Event B: randomly selecting a senior
b. Event A: randomly selecting a doctor Event B: randomly selecting a female
c. Event A: A
Event B: A’
2. Each teacher cast one vote for the teacher of the year. Of the teachers 25% voted for Goodwin,
20% for Kline, and 55% for Alonzo. If a voting teacher is selected at random, what is the
probability that they voted for Kline or Alonzo?
3. A drink company applies one label to each bottle cap: “free drink,” “free meal,” or try again.” A
bottle cap has a 1/10 probability of being labeled “free drink” and a 1/25 probability of being
labeled “free meal.” What is the probability that a bottle cap is labeled “free drink” or “free
meal?”
4. Find each probability on a die.
a. Rolling a 5 or an odd number.
b. Rolling at least one 4 when rolling 2 dice.
5. A poll showed that 61% of Americans say they believe that life exists elsewhere in the galaxy.
What is the probability of randomly selecting someone NOT having that belief?
6. The table below shows the number of passengers that survived or died during the Titanic
catastrophe.
Men
Women
Boys
Girls
Total
Survived
332
318
29
27
706
Died
1360
104
35
18
1517
Total
1592
422
64
45
2223
a.
b.
c.
d.
e.
f.
Find the probability of selecting a man.
Find the probability of selecting a passenger who survived.
Find the probability of selecting a man or woman.
Find the probability of selecting a woman or someone who survived.
Find the probability of selecting a boy or someone who died.
Find the probability of selecting a man or someone who died.
7. A group of juniors and seniors were polled to find out how many were planning to major in a
scientific study in college. 210 Juniors and 200 Seniors voted no. Find each of the probabilities if
a student is selected at random.
Yes
No
Total
Junior
360
Senior
312
Total
a.
b.
c.
d.
e.
P(Junior)
P(Yes)
P(Senior or Yes)
P(Junior or No)
P(not Senior)
8. Of 3510 drivers surveyed, 1950 were male and 103 were color-blind. Only 6 of the color-blind
drivers were female. What is the probability that a driver was male or was color-blind.
Addition Rule Answers 1. 7/22 2. 4/11 3. 15/22 4. 6/11 5. 19/22 6. 122/1000 7. 520/1000 8. 745/1000 9. 450/1000 10. 768/1000 11. 6/10 12. 7/10 13. 7/10 14. 3/10 15. 5/10 Conditional Probability Answers 1. .667 2. .576 3. .714 4. .625 5. .455 6. .0714 7. .214 8. .632 9. .6 10. .19 11. .387 12. .3 13. .683 14. .317 8
2
68
15. .613 16. .7 17. .406 18. .12 19. 20. 21. 9
3
75
2
1
5
4
22. 23. a) b) c) 3
2
19
21
Independent/Dependent Answers 1 Independent 2 Independent 3 Independent 4 Independent 5 Dependent 6 .0833 7 .333 8 .0833 9 .25 10 .167 11 .167 12 .333 13 .286 14 .143 15 .190 16 .381 17 .0741 18 .198 19 .0988 20 .0494 21 .0370 22 .0833 23 .167 24 .111 25 .0278 26 .0119 ADDITION RULE 2ANSWERS
1. a. mutually exclusive b. inclusive
c. mutually exclusive
2. 0.75
3. 0.14
4a. 0.5
4b. 0.306
6a. 0.716
6b. 0.318
6c. 0.906
6d. 6d. 0.364
6e. 0.695
7c. 0.688
7d. 0.833
7a. 0.223
8. 0.557
7b. 0.390
5. .39
6f. 0.787