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4.3 – Probability Using Sets – Worksheet MDM4U Jensen 1. Using the Venn diagram below, list the elements (numbers) found in each of the following sets. a) 𝑃 ∩ 𝑄 b) 𝑃 ∪ 𝑄 c) 𝑋 ∩ 𝑄 d) 𝑋 ∪ 𝑄 e) 𝑌 ∩ 𝑄 f) 𝑃 ∩ 𝑄 ∩ 𝑋 2. For each of the following, find the indicated probability and state whether 𝐴 and 𝐵 are mutually exclusive. a) 𝑃 𝐴 = 0.5, 𝑃 𝐵 = 0.2, 𝑃 𝐴 ∪ 𝐵 = 0.7, 𝑃 𝐴 ∩ 𝐵 =? b) 𝑃 𝐴 = 0.7, 𝑃 𝐵 = 0.2, 𝑃 𝐴 ∪ 𝐵 =? , 𝑃 𝐴 ∩ 𝐵 = 0.15 c) 𝑃 𝐴 = 0.3, 𝑃 𝐵 =? , 𝑃 𝐴 ∪ 𝐵 = 0.9, 𝑃 𝐴 ∩ 𝐵 = 0 !
3. The probability that Kelly will make the volleyball team is ! and the probability that she will make the !
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field hockey team is !. If the probability that she makes both teams is !, what is the probability that she makes at least one of the teams? 4. An aquarium at a pet store contains 20 guppies (12 females and 8 males) and 36 tetras (14 females and 22 males). If the clerk randomly nets a fish, what is the probability that it is a female or a tetra? 5. An automobile manufacturer estimates the probability of a mechanical defect in the one year warranty period is 0.65. The probability of any other defect is 0.35. The probability of encountering both types of defect is 0.20. What is the probability of encountering any type of defect? 6. At the start of flue season, Dr. Anna Ahmeed examines 50 patients over two days. Of those 50 patients, 30 have a headache, 24 have a cold, and 12 have neither symptom. Some patients have both symptoms. a) Draw a Venn diagram and determine the number of patients that have both symptoms. b) Find the probability that a patient selected at random… i) has just a headache ii) has a headache or a cold iii) does not have cold symptoms 7. a) Use the table to complete the following Venn Diagram: # of Team Students Volleyball 15 Basketball 12 Swimming 10 VB and BB 8 VB and Swim 4 BB and Swim 4 All three 3 b) What is the probability that a student plays volleyball? c) What is the probability that a student plays basketball? d) What is the probability that a student plays basketball and volleyball? e) What is the probability that a student plays basketball or volleyball? 8. Find the probability that, when you draw a single card from a well-­‐shuffled standard deck of 52 playing cards, you choose an ace or a club. 9. The probability it will rain today is 0.4 and the probability it will rain tomorrow is 0.3. The probability it will rain both days is 0.2. What is the probability it will rain today or tomorrow? 10. The frequency distribution shows the volume of sales (in dollars) and the number of months a sales representative reached each sales level during the past three years. If this sales pattern continues, what is the probability that the sales representative will sell between $75000 and $124999 next month? Sales volume ($) Months 0 – 24 999 3 25 000 – 49 999 5 50 000 – 74 999 6 75 000 – 99 999 7 100 000 – 124 999 9 125 000 – 149 999 2 150 000 – 174 999 3 175 000 – 199 999 1 11. A blood bank catalogs the types of blood, including positive or negative Rh-­‐factor, given by donors during the last five days. The number of donors who gave each blood type is shown in the table. A donor is selected at random. a) Find the probability that the donor has type O or type A blood. b) Find the probability that the donor has type B blood or is Rh-­‐negative. Answers 1. a) {6, 9} b) {2, 5, 6, 9, 10, 12} c) {9, 10} d) {2, 4, 6, 9, 10, 12} e) ∅ f) {9} 2. a) 𝑃 𝐴 ∩ 𝐵 = 0, mutually exclusive b) 𝑃 𝐴 ∪ 𝐵 = 0.75, not mutually exclusive c) 𝑃 𝐵 = 0.6, mutually exclusive !!
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6. a) b) i) !" ii) !" iii) !" !
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7. a) b) ! c) ! d) ! e) !" !
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10. ! 11. a) 0.851 b) 0.249