Venn Diagrams

Question 1 1. In a class of 50 students, 18 take Chorus, 26 take Band, and 2 take both Chorus and Band.  How many students in the class are not enrolled in either Chorus or Band?

Question 2 2. In a school of 320 students, 85 students are in the band, 200 students are on sports teams, and 60 students participate in both activities.  How many students are involved in either band or sports?

Question 2a From a survey of 100 college students, a marketing research company found that 75 students owned stereos, 45 owned cars, and 35 owned cars and stereos. How many students owned either a car or a stereo?

Question 2B From a survey of 100 college students, a marketing research company found that 75 students owned stereos, 45 owned cars, and 35 owned cars and stereos. How many students did not own a car or a stereo?

Question 3 3. A veterinarian surveys 26 of his patrons.  He discovers that 14 have dogs, 10 have cats, and 5 have fish.  Four have dogs and cats, 3 have dogs and fish, and one has a cat and fish.  If no one has all three kinds of pets, how many patrons have none of these pets?

Question 4 4. A guidance counselor is planning schedules for 30 students.  Sixteen students say they want to take French, 16 want to take Spanish, and 11 want to take Latin.  Five say they want to take both French and Latin, and of these, 3 wanted to take Spanish as well.  Five want only Latin, and 8 want only Spanish.  How many students want French only?

Question 5 4. 100 students were interviewed. 28 take Physical Education, 31 take Biology, 42 take English, 9 take PE and BIO, 10 take PE and English, 6 took BIO and ENG and 4 take all 3 classes. 1.) How many students took none of the 3 subjects?

Question 6 4. 100 students were interviewed. 28 take Physical Education, 31 take Biology, 42 take English, 9 take PE and BIO, 10 take PE and English, 6 took BIO and ENG and 4 take all 3 classes. 2.) How many students took PE but not BIO or ENG?

Question 7 4. 100 students were interviewed. 28 take Physical Education, 31 take Biology, 42 take English, 9 take PE and BIO, 10 take PE and English, 6 took BIO and ENG and 4 take all 3 classes. 3.) How many students took BIO and PE but not English?

Question 8 My cat has a taste for adorable little geckoes. In one month, suppose he deposited: 6 gray geckoes, 12 geckoes that had dropped their tails, and 15 geckoes that he'd chewed on a little. Only 1 of the geckoes was gray, chewed on, and tailless; 2 were gray and tailless but not chewed on; 2 were gray and chewed on but not tailless. If there were a total of 24 geckoes left on my carpet that month. How many were tailless and chewed on but not gray? Use a 3 circle Venn diagram.

Question 9 At Dawnview High there are 400 Grade 11 learners. 270 do Computer Science, 300 do English and 50 do Business studies. All those doing Computer Science do English, 20 take Computer Science and Business studies and 35 take English and Business studies. How many students only take English?

Try it yourself 1 1.) Event A: Randomly select a jack from a standard deck of cards. Event B: Randomly select a face card from a standard deck of cards. a.) Decide if one of the following statements is true. Events A and B can not occur at the same time. Is not true – Events A and B can happen at the same time.

Try it yourself 1 1.) Event A: Randomly select a jack from a standard deck of cards. Event B: Randomly select a face card from a standard deck of cards. a.) Decide if one of the following statements is true. Events A and B have no outcomes in common. Is not true – Events A and B share on outcome.

Try it yourself 1 1.) Event A: Randomly select a jack from a standard deck of cards. Event B: Randomly select a face card from a standard deck of cards. a.) Decide if one of the following statements is true. P(A and B) = 0 Is not true - 𝑃 𝐴 ∙𝑃 𝐵 = 4 52 ∙ 12 52 =0.018≠0

Try it yourself 1 1.) Event A: Randomly select a jack from a standard deck of cards. Event B: Randomly select a face card from a standard deck of cards. b.) Make a conclusion. A and B are not mutually exclusive

2.) Event A: Randomly select a 20-year old student Event B: Randomly select a student with blue eyes Events A and B cannot occur at the same time. Is not true – A and B can occur at the same time. Events A and B have no outcomes in common. Is not true – Events A and B have an outcome in common. 𝑃 𝐴 𝑎𝑛𝑑 𝐵 =0 Is not true - 𝑃 𝐴 ∙𝑃 𝐵 ≠0 b.) Conclude that Events A and B are not mutually exclusive.

2. ) Event A: Randomly select a vehicle that is a Ford 2.) Event A: Randomly select a vehicle that is a Ford. Event B: randomly select a vehicle that is a Toyota. Events A and B cannot occur at the same time. True– A and B cannot occur at the same time. Events A and B have no outcomes in common. True– Events A and B have no outcomes in common. 𝑃 𝐴 𝑎𝑛𝑑 𝐵 =0 No union exists

Mutually exclusive 3.3

To be or not to be

Addition property “or” 𝑃 𝐴 𝑜𝑟 𝐵 =𝑃 𝐴 +𝑃 𝐵 −𝑃 𝐴 𝑎𝑛𝑑 𝐵 Unless Event A and B are mutually exclusive then 𝑃 𝐴 𝑜𝑟 𝐵 =𝑃 𝐴 +𝑃 𝐵

Decide 1.) Are the events mutually exclusive 2.) If yes then 𝑃 𝐴 𝑜𝑟 𝐵 =𝑃 𝐴 +𝑃 𝐵 −𝑃 𝐴 𝑎𝑛𝑑 𝐵 3.) If no then 𝑃 𝐴 𝑜𝑟 𝐵 =𝑃 𝐴 +𝑃 𝐵

Homework page 145 1.) P(A and B)=o because A and B can not happen at the same time. 2.) Mutually Exclusive Example Event A – Toss a Heads Event B – Toss a Tails Non Mutually Exclusive Example Event A – Drawing an Ace Event B – Drawing a Spade

homework 3.) True 4.) False. Two independent Events does not mean they are mutually exclusive. 5.) false. 𝑃 𝐴 𝑜𝑟 𝐵 =𝑃 𝐴 +𝑃 𝐵 −𝑃 𝐴 𝒂𝒏𝒅 𝐵 6.) true. 7.) Not mutually exclusive 8.) mutually exclusive 9.) not mutually exclusive 10.) not mutually exclusive 11.) mutually exclusive 12.) not mutually exclusive

homework 13a.) Not mutually exclusive because 5 weeks the events overlapped. 13b.) 𝑃 𝐴 𝑜𝑟 𝐵 =𝑃 𝐴 +𝑃 𝐵 −𝑃 𝐴 𝑎𝑛𝑑 𝐵 𝑃 𝐴 𝑜𝑟 𝐵 = 18 52 + 9 52 − 5 52 𝑃 𝐴 𝑜𝑟 𝐵 = 11 26 ≈.423

homework 14a.) Not mutually exclusive 14b.) 𝑃 𝐴 𝑜𝑟 𝐵 =𝑃 𝐴 +𝑃 𝐵 −𝑃 𝐴 𝑎𝑛𝑑 𝐵 𝑃 𝐴 𝑜𝑟 𝐵 = 1800 3500 + 860 3500 − 425 3500 𝑃 𝐴 𝑜𝑟 𝐵 = 2235 3500 ≈.639

homework 15a.) Not mutually exclusive 15b.) 𝑃 𝐴 𝑜𝑟 𝐵 =𝑃 𝐴 +𝑃 𝐵 −𝑃 𝐴 𝑎𝑛𝑑 𝐵 𝑃 𝐴 𝑜𝑟 𝐵 =0.05+0.08−0.004 𝑃 𝐴 𝑜𝑟 𝐵 =0.126

homework 16a.) Not mutually exclusive because a can could have no punctures or smashed edges. 16b.) 𝑃 𝐴 𝑜𝑟 𝐵 =𝑃 𝐴 +𝑃 𝐵 −𝑃 𝐴 𝑎𝑛𝑑 𝐵 𝑃 𝐴 𝑜𝑟 𝐵 =0.96+0.93−0.893 𝑃 𝐴 𝑜𝑟 𝐵 =0.997

homework 17a.) 𝑃 𝐻𝑒𝑎𝑟𝑡 = 13 52 𝑃 3 = 4 52 𝑃 𝐻𝑒𝑎𝑟𝑡 𝑎𝑛𝑑 3 = 1 52 𝑃 𝐻𝑒𝑎𝑟𝑡 𝑜𝑟 3 = 13 52 + 4 52 − 1 52 ≈0.308 17b.) 𝑃 𝐵𝑙𝑎𝑐𝑘 𝑠𝑢𝑖𝑡 = 26 52 𝑃 𝐾𝑖𝑛𝑔 = 4 52 𝑃 𝐵𝑙𝑎𝑐𝑘 𝑆𝑢𝑖𝑡 𝑎𝑛𝑑 𝐾𝑖𝑛𝑔 = 2 52 𝑃 𝐵𝑙𝑎𝑐𝑘 𝑆𝑢𝑖𝑡 𝑜𝑟 𝐾𝑖𝑛𝑔 = 26 52 + 4 52 − 2 52 ≈0.538

homework 17c.) 𝑃 5 = 4 52 𝑃 𝐹 = 12 52 𝑃 5 𝑎𝑛𝑑 𝐹 =0 𝑃 5 𝑜𝑟 𝐹 = 4 52 + 12 52 ≈0.308

homework 18a.) 𝑃 6 = 1 6 𝑃 >4 = 2 6 𝑃 6 𝑎𝑛𝑑>4 = 1 6 𝑃 6 𝑜𝑟>4 = 1 6 + 2 6 − 1 6 ≈0.334 18b.) 𝑃 <5 = 4 6 𝑃 𝑂𝑑𝑑 = 3 6 𝑃 <5 𝑎𝑛𝑑 𝑜𝑑𝑑 = 2 6 𝑃 <5 𝑜𝑟 𝑜𝑑𝑑 = 4 6 + 3 6 − 2 6 ≈0.833

homework 18c.) 𝑃 3 = 1 6 𝑃 𝑒𝑣𝑒𝑛 = 3 6 𝑃 3 𝑎𝑛𝑑 𝑒𝑣𝑒𝑛 =0 𝑃 3 𝑜𝑟 𝑒𝑣𝑒𝑛 = 1 6 + 3 6 ≈0.667

Homework 19a.) 𝑃 𝑢𝑛𝑑𝑒𝑟 5 =6.7% 19b.) 𝑃 𝑛𝑜𝑡 65 𝑦𝑒𝑎𝑟𝑠 𝑜𝑟 𝑜𝑣𝑒𝑟 =100−13.2=86.8% 19c.) 23.1% 20a.) 29.8% 20b.) 44.5% 20c.) 43.5% 21a.) 11% 21b.) 72%

homework 22a.) 17% 24a.) .4% 22b) 62.1% 24b.) .3% 24c.) 21.4% 23a.) 14.3% 24d.) .3% 23b.) 77.4% 24e.) .6% 23c.) 22.6%