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3.3-The Addition Rule

3.3-The Addition Rule. Mutually Exclusive Events : can NOT occur at the same time. A and B. A and B are Mutually exclusive. A and B are NOT Mutually exclusive. Are these events mutually exclusive?. 1. A= roll a 3 on a die B = roll a 4 on a die.

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3.3-The Addition Rule

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  1. 3.3-The Addition Rule • Mutually Exclusive Events: can NOT occur at the same time A and B A and B are Mutually exclusive A and B are NOT Mutually exclusive

  2. Are these events mutually exclusive? • 1. A= roll a 3 on a die B = roll a 4 on a die. • 2. A= roll a 3 on a die B = roll an even # on die • 3. Select a student A=male B=nursing major • 4. Select blood donor A=type O B=female

  3. Are these events mutually exclusive? • 1. A= roll a 3 on a die B = roll a 4 on a die. Yes – can’t occur at same time • 2. A= roll a 3 on a die B = roll an even # on die • 3. Select a student A=male B=nursing major • 4. Select blood donor A=type O B=female

  4. Are these events mutually exclusive? • 1. A= roll a 3 on a die B = roll a 4 on a die. Yes – can’t occur at same time • 2. A= roll a 3 on a die B = roll an even # on die Yes – can’t occur at same time • 3. Select a student A=male B=nursing major • 4. Select blood donor A=type O B=female

  5. Are these events mutually exclusive? • 1. A= roll a 3 on a die B = roll a 4 on a die. Yes – can’t occur at same time • 2. A= roll a 3 on a die B = roll an even # on die Yes – can’t occur at same time • 3. Select a student A=male B=nursing major No- could be both at same time • 4. Select blood donor A=type O B=female

  6. Are these events mutually exclusive? • 1. A= roll a 3 on a die B = roll a 4 on a die. Yes – can’t occur at same time • 2. A= roll a 3 on a die B = roll an even # on die Yes – can’t occur at same time • 3. Select a student A=male B=nursing major No- could be both at same time • 4. Select blood donor A=type O B=female No – could be both at same time

  7. Are these events mutually exclusive? • 1. Select a card A=Jack B=Face card • 2. Select student A=20 yr. B=blue eyes • 3. Select car A=Ford B=Toyota

  8. Are these events mutually exclusive? • 1. Select a card A=Jack B=Face card No – a jack is BOTH • 2. Select student A=20 yr. B=blue eyes • 3. Select car A=Ford B=Toyota

  9. Are these events mutually exclusive? • 1. Select a card A=Jack B=Face card No – a jack is BOTH • 2. Select student A=20 yr. B=blue eyes NO – could be BOTH 20 and blue eyed • 3. Select car A=Ford B=Toyota

  10. Are these events mutually exclusive? • 1. Select a card A=Jack B=Face card No – a jack is BOTH • 2. Select student A=20 yr. B=blue eyes NO – could be BOTH 20 and blue eyed • 3. Select car A=Ford B=Toyota YES – can’t be both at same time

  11. Addition Rule: P(A OR B) • If events A OR B will occur • 1 OR the other, or both! P(A OR B)= P(A) + P(B) – P(A AND B) Subtracting P(A AND B) avoids double counting outcomes that occur in BOTH A and B • IF Mutually exclusive: P(A OR B) = P(A) + P(B)

  12. Examples: Find the Probability • 1. Select a card. Probability the card is a 4 OR an ace. • 2. Roll die. Probability rolling a 6 OR an odd. • 3. Roll a die. Probability rolling a # less than 3 OR odd. • 4. Select a card. Probability the card a face card OR a heart.

  13. Examples: Find the Probability • 1. Select a card. Probability the card is a 4 OR an ace. Mutually exclusive P(4 OR Ace)=P(4)+P(A)=4/52 + 4/52=.154 • 2. Roll die. Probability rolling a 6 OR an odd. • 3. Roll a die. Probability rolling a # less than 3 OR odd. • 4. Select a card. Probability the card a face card OR a heart.

  14. Examples: Find the Probability • 1. Select a card. Probability the card is a 4 OR an ace. Mutually exclusive P(4 OR Ace)=P(4)+P(A)=4/52 + 4/52=.154 • 2. Roll die. Probability rolling a 6 OR an odd. P(6 OR odd)= P(6)+P(odd)=1/6+3/6=.667 • 3. Roll a die. Probability rolling a # less than 3 OR odd. • 4. Select a card. Probability the card a face card OR a heart.

  15. Examples: Find the Probability • 1. Select a card. Probability the card is a 4 OR an ace. Mutually exclusive P(4 OR Ace)=P(4)+P(A)=4/52 + 4/52=.154 • 2. Roll die. Probability rolling a 6 OR an odd. P(6 OR odd)= P(6)+P(odd)=1/6+3/6=.667 • 3. Roll a die. Probability rolling a # less than 3 OR odd. P(<3 OR odd)= P(<3)+P(odd) – P(<3 AND odd) 2/6+ 3/6 – (1/6) = 5/6-1/6=4/6=.667 • 4. Select a card. Probability the card a face card OR a heart.

  16. Examples: Find the Probability • 1. Select a card. Probability the card is a 4 OR an ace. Mutually exclusive P(4 OR Ace)=P(4)+P(A)=4/52 + 4/52=.154 • 2. Roll die. Probability rolling a 6 OR an odd. P(6 OR odd)= P(6)+P(odd)=1/6+3/6=.667 • 3. Roll a die. Probability rolling a # less than 3 OR odd. P(<3 OR odd)= P(<3)+P(odd) – P(<3 AND odd) 2/6+ 3/6 – (1/6) = 5/6-1/6=4/6=.667 • 4. Select a card. Probability the card a face card OR a heart. P(face OR heart) = P(face)+P(heart)-P(f AND h) 12/52+13/52 –(3/52) = 22/52=.423

  17. Examples: • Probability a rep will have sales between $75,000 and $124,000 next month. • Probability a rep will have sales between $0 and $49,000 next month.

  18. Examples: • Probability a rep will have sales between $75,000 and $124,000 next month. (exclusive) P(C OR D)=P(C)+P(D) = 7/36+9/36=.444 2. Probability a rep will have sales between $0 and $49,000 next month. A = sales between 0-$24,999 B= sales between $25,000-$49,999 C=sales between $75,000-$99,999 D=sales between $100,000-$124,999 Total months 36

  19. Examples: • Probability a rep will have sales between $75,000 and $124,000 next month. (exclusive) P(C OR D)=P(C)+P(D) = 7/36+9/36=.444 • Probability a rep will have sales between $0 and $49,000 next month.(exclusive) 3/36+5/36=.222 A = sales between 0-$24,999 B= sales between $25,000-$49,999 C=sales between $75,000-$99,999 D=sales between $100,000-$124,999

  20. Examples: Find the Probability Blood type Rh • 1. Type O OR A • 2. Type B OR AB • 3. Type B OR Rh-negative • 4. Type O OR Rh-positive

  21. Examples: Find the Probability Blood type Rh • 1. Type O OR A (exclusive) P(O OR A)= P(O)+P(A)=184/409+164/409=348/409=.85 • 2. Type B OR AB • 3. Type B OR Rh-negative • 4. Type O OR Rh-positive

  22. Examples: Find the Probability Blood type Rh • 1. Type O OR A (exclusive) P(O OR A)= P(O)+P(A)=184/409+164/409=348/409=.85 • 2. Type B OR AB (exclusive) P(B OR AB)=P(B)+P(AB)=45/409+16/409=61/409=.149 • 3. Type B OR Rh-negative • 4. Type O OR Rh-positive

  23. Examples: Find the Probability Blood type Rh • 1. Type O OR A (exclusive) P(O OR A)= P(O)+P(A)=184/409+164/409=348/409=.85 • 2. Type B OR AB (exclusive) P(B OR AB)=P(B)+P(AB)=45/409+16/409=61/409=.149 • 3. Type B OR Rh-negative P(B OR -)=P(B)+P(-)-P(B & -)=45/409+65/409-8/409=.249 • 4. Type O OR Rh-positive

  24. Examples: Find the Probability Blood type Rh • 1. Type O OR A (exclusive) P(O OR A)= P(O)+P(A)=184/409+164/409=348/409=.85 • 2. Type B OR AB (exclusive) P(B OR AB)=P(B)+P(AB)=45/409+16/409=61/409=.149 • 3. Type B OR Rh-negative P(B OR -)=P(B)+P(-)-P(B & -)=45/409+65/409-8/409=.249 • 4. Type O OR Rh-positive P(O Or +)=P(O)+P(+)-P(O&+)=184/409+344/409-156/409=.910

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