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

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Presentation transcript:

3.3-The Addition Rule Mutually Exclusive Events: can NOT occur at the same time A B AB 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. 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

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

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

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

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

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

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

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

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

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)

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.

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= 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.

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= Roll die. Probability rolling a 6 OR an odd. P(6 OR odd)= P(6)+P(odd)=1/6+3/6= Roll a die. Probability rolling a # less than 3 OR odd. 4. Select a card. Probability the card a face card OR a heart.

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= Roll die. Probability rolling a 6 OR an odd. P(6 OR odd)= P(6)+P(odd)=1/6+3/6= 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= Select a card. Probability the card a face card OR a heart.

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= Roll die. Probability rolling a 6 OR an odd. P(6 OR odd)= P(6)+P(odd)=1/6+3/6= 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= 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

Examples: 1.Probability a rep will have sales between $75,000 and $124,000 next month. 2.Probability a rep will have sales between $0 and $49,000 next month. SalesMonths 0-24, ,000-49, ,000-74, ,000-99, , , , , , , , ,0001

Examples: 1.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= Probability a rep will have sales between $0 and $49,000 next month. SalesMonths 0-24, ,000-49, ,000-74, ,000-99, , , , , , , , ,0001 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

Examples: 1.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= Probability a rep will have sales between $0 and $49,000 next month.(exclusive) 3/36+5/36=.222 SalesMonths 0-24, ,000-49, ,000-74, ,000-99, , , , , , , , ,0001 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

Examples: Find the Probability Rh 1. Type O OR A 2. Type B OR AB 3. Type B OR Rh-negative 4. Type O OR Rh-positive OABABTotal Positive Negative Total Blood type

Examples: Find the Probability Rh 1. Type O OR A (exclusive) P(O OR A)= P(O)+P(A)=184/ /409=348/409= Type B OR AB 3. Type B OR Rh-negative 4. Type O OR Rh-positive OABABTotal Positive Negative Total Blood type

Examples: Find the Probability Rh 1. Type O OR A (exclusive) P(O OR A)= P(O)+P(A)=184/ /409=348/409= Type B OR AB (exclusive) P(B OR AB)=P(B)+P(AB)=45/409+16/409=61/409= Type B OR Rh-negative 4. Type O OR Rh-positive OABABTotal Positive Negative Total Blood type

Examples: Find the Probability Rh 1. Type O OR A (exclusive) P(O OR A)= P(O)+P(A)=184/ /409=348/409= Type B OR AB (exclusive) P(B OR AB)=P(B)+P(AB)=45/409+16/409=61/409= Type B OR Rh-negative P(B OR -)=P(B)+P(-)-P(B & -)=45/409+65/409-8/409= Type O OR Rh-positive OABABTotal Positive Negative Total Blood type

Examples: Find the Probability Rh 1. Type O OR A (exclusive) P(O OR A)= P(O)+P(A)=184/ /409=348/409= Type B OR AB (exclusive) P(B OR AB)=P(B)+P(AB)=45/409+16/409=61/409= Type B OR Rh-negative P(B OR -)=P(B)+P(-)-P(B & -)=45/409+65/409-8/409= Type O OR Rh-positive P(O Or +)=P(O)+P(+)-P(O&+)=184/ / /409=.910 OABABTotal Positive Negative Total Blood type