1. Mutually Exclusive Events OBJ: Find the probability that mutually exclusive and inclusive events occur

2. Addition Rule P (A or B) P (A U B) = P(A) + P(B)–P(A∩B) P (A and B) P (A ∩ B)

3. DEF:  Mutually Exclusive Events 2 events that cannot both occur at the same time; P (A and B) = 0 P (A ∩ B) = 0 Impossible event P (A or B) P(A U B)=P(A)+P(B)

4. EX:  In a throw of 2 dice, what is the probability of obtaining a sum of 7 or 11 6 (sums of 7) 36 (sums) 2 (sums of 11) 36 (sums) 6 + 2 36 36 8 36 = 2 9 234567 345678 456789 5678910 6789 11 789101112

5. EX:  In a throw of a red die, r, and a white die, w, find: P (sum of 6 or sum of 10) 5 (sums of 6) 36 (sums) 3 (sums of 10) 36 (sums) 5 + 3 36 36 8 36 = 2 9 234567 345678 456789 5678910 6789 11 789101112

6. DEF:  Inclusive Events 2 events that can both occur at the same time P (A or B) P (A U B) = P(A) + P(B)–P(A∩B)

7. EX:  In a throw of a red die, r, and a white die, w, find: P (r ≤ 3 or w = 2) P (r ≤ 3) 18 (r  3) 36 (die pairs) P (w = 2) 6 (w = 2) 36 (die pairs) P (r ≤ 3 and w = 2) P (r  3 ∩ w = 2) 3 36 P (r ≤ 3 or w = 2) P (r ≤ 3) + P (w = 2)–P (r ≤ 3 ∩ w = 2) 18 + 6 – 3 36 36 36 21 36 7 12 (1, 1)(1,2)(1, 3)(1, 4)(1, 5)(1, 6) (2, 1)(2, 2)(2, 3)(2, 4)(2, 5)(2, 6) (3, 1)(3, 2)(3, 3)(3, 4)(3, 5)(3, 6) (4, 1)(4, 2)(4, 3)(4, 4)(4, 5)(4, 6) (5, 1)(5, 2)(5, 3)(5, 4)(5, 5)(5, 6) (6, 1)(6, 2)(6, 3)(6, 4)(6, 5)(6, 6)

8. EX:  In a throw of a red die, r, and a white die, w, find: P (r ≥ 3 or w ≥ 5) P (r ≥ 3) 24 (r  3) 36 (die pairs) P (w ≥ 5) 12 (w  5) 36 (die pairs) P (r ≥ 3 and w ≥ 5) P (r  3 ∩ w  5) 8 36 P (r ≥ 3 or w ≥ 5) P (r ≥ 3) + P (w ≥ 5)–P (r ≥ 3 ∩ w ≥ 5) 24 + 12 – 8 36 36 36 28 36 7 9 (1, 1)(1,2)(1, 3)(1, 4)(1, 5)(1, 6) (2, 1)(2, 2)(2, 3)(2, 4)(2, 5)(2, 6) (3, 1)(3, 2)(3, 3)(3, 4)(3, 5)(3, 6) (4, 1)(4, 2)(4, 3)(4, 4)(4, 5)(4, 6) (5, 1)(5, 2)(5, 3)(5, 4)(5, 5)(5, 6) (6, 1)(6, 2)(6, 3)(6, 4)(6, 5)(6, 6)

9. EX:  A card is drawn from an ordinary deck. Find: P (red or a queen) 26 + 4 – 2 52 52 52 28 52 7 13 P(black king or a club) 2 + 13 – 1 52 52 52 14 52 7 26

10. EX:  A card is drawn from an ordinary deck. Find: P(an even number or black) 20 + 26 – 10 52 52 52 36 52 9 13 P (red face or a jack) 6 + 4 – 2 52 52 52 8 52 2 13

11. EX:  In a throw of a red die, r, and a white die, w, find: Worksheet 1. P (sum = 7 or red die = 3) P (sum = 7) 6 36 P (red die = 3) 6 36 P (sum = 7 and red die = 3 16 6 + 6 – 1 36 36 36 11 36 (1, 1)(1,2)(1, 3)(1, 4)(1, 5)(1, 6) (2, 1)(2, 2)(2, 3)(2, 4)(2, 5)(2, 6) (3, 1)(3, 2)(3, 3)(3, 4)(3, 5)(3, 6) (4, 1)(4, 2)(4, 3)(4, 4)(4, 5)(4, 6) (5, 1)(5, 2)(5, 3)(5, 4)(5, 5)(5, 6) (6, 1)(6, 2)(6, 3)(6, 4)(6, 5)(6, 6) 234567 345678 456789 5678910 6789 11 789101112

12. EX:  In a throw of a red die, r, and a white die, w, find: Worksheet 2. P (sum = 10 and red die = 4) P (sum = 10) 3 = 1 (reduce since multi.) 36 12 P (red die = 4) 6 = 1 36 6 1 1 (and →multiply) 12 6 2(1/72) 1 36 (1, 1)(1,2)(1, 3)(1, 4)(1, 5)(1, 6) (2, 1)(2, 2)(2, 3)(2, 4)(2, 5)(2, 6) (3, 1)(3, 2)(3, 3)(3, 4)(3, 5)(3, 6) (4, 1)(4, 2)(4, 3)(4, 4)(4, 5)(4, 6) (5, 1)(5, 2)(5, 3)(5, 4)(5, 5)(5, 6) (6, 1)(6, 2)(6, 3)(6, 4)(6, 5)(6, 6) 234567 345678 456789 5678910 6789 11 789101112

13. EX:  In a throw of a red die, r, and a green die, g, find: Worksheet 4. P (r > 5 or g < 2) P (r > 5) 6 36 P (g < 2) 6 36 3. P (r > 5 and g < 2) 1 1(and →multiply) 6 6 6 + 6 – 1 36 36 36 11 36 (1, 1)(1,2)(1, 3)(1, 4)(1, 5)(1, 6) (2, 1)(2, 2)(2, 3)(2, 4)(2, 5)(2, 6) (3, 1)(3, 2)(3, 3)(3, 4)(3, 5)(3, 6) (4, 1)(4, 2)(4, 3)(4, 4)(4, 5)(4, 6) (5, 1)(5, 2)(5, 3)(5, 4)(5, 5)(5, 6) (6, 1)(6, 2)(6, 3)(6, 4)(6, 5)(6, 6)

14. EX:  In a throw of a red die, r, and a green die, g, find: 8.P (sum is prime or sum <6) P (sum is prime) 15 (prime sums) 36 (sums) P (sum <6) 10 (sums < 6) 36 (sums) P (sum is prime & sum < 6) 7 36 15 + 10 – 7 36 36 36 18/36 = ½ 234567 345678 456789 5678910 6789 11 789101112

15. EX:  A card is drawn from an ordinary deck. Find: Worksheet (9) P (king or club) 4 + 13 – 1 (10) 52 52 52 16 52 4 13 Worksheet (11) P (king or queen) 4 + 4 (12) 0 52 8 2 13

16. Worksheet: Select a number between 1 and 100 (inclusive) (18) P (prime) 25 100 1 4 (19) P (less than 50) 49 100 (20) P (prime and < 50) 15 100 3 20 (21) P (prime or < 50) 25 + 49 – 15 100 100100 59 100