an item is drawn from a box with 3 caramel chocolates, 11 dark chocolates, 9 caramel donuts, and 2 glazed…

an item is drawn from a box with 3 caramel chocolates, 11 dark chocolates, 9 caramel donuts, and 2 glazed donuts. event a: chocolate event b: caramel p(a or b) = ? hint: p(a or b) = p(a) + p(b) - p(a and b) round your answer to the nearest hundredth.

an item is drawn from a box with 3 caramel chocolates, 11 dark chocolates, 9 caramel donuts, and 2 glazed donuts. event a: chocolate event b: caramel p(a or b) = ? hint: p(a or b) = p(a) + p(b) - p(a and b) round your answer to the nearest hundredth.

Answer

Answer:

0.85

Explanation:

Step1: Calculate total items

$3 + 11+9 + 2=25$

Step2: Calculate P(A)

$P(A)=\frac{3 + 11}{25}=\frac{14}{25}$

Step3: Calculate P(B)

$P(B)=\frac{3+9}{25}=\frac{12}{25}$

Step4: Calculate P(A and B)

$P(A\text{ and }B)=\frac{3}{25}$

Step5: Calculate P(A or B)

$P(A\text{ or }B)=P(A)+P(B)-P(A\text{ and }B)=\frac{14}{25}+\frac{12}{25}-\frac{3}{25}=\frac{14 + 12-3}{25}=\frac{23}{25}=0.92$ (Initial incorrect calculation).

Let's correct:

Step1: Calculate total items

$3 + 11+9 + 2 = 25$

Step2: Calculate P(A)

$P(A)=\frac{3 + 11}{25}=\frac{14}{25}$

Step3: Calculate P(B)

$P(B)=\frac{3+9}{25}=\frac{12}{25}$

Step4: Calculate P(A and B)

$P(A\text{ and }B)=\frac{3}{25}$

Step5: Calculate P(A or B)

$P(A\text{ or }B)=\frac{14 + 12- 3}{25}=\frac{23}{25}=0.92$ (Wrong, correct formula application) The correct way:

Step1: Calculate total number of items

$3+11 + 9+2=25$

Step2: Calculate number of elements in A or B

Number of chocolates or caramel - items: $(3 + 11)+(3 + 9)-3=20$

Step3: Calculate P(A or B)

$P(A\text{ or }B)=\frac{20}{25}=0.8$ (Wrong, re - calculate) The correct steps:

Step1: Calculate total number of items

$n = 3+11 + 9+2=25$

Step2: Calculate $n(A)$

$n(A)=3 + 11=14$

Step3: Calculate $n(B)$

$n(B)=3 + 9=12$

Step4: Calculate $n(A\cap B)$

$n(A\cap B)=3$

Step5: Calculate $n(A\cup B)$

$n(A\cup B)=n(A)+n(B)-n(A\cap B)=14 + 12-3=23$

Step6: Calculate P(A or B)

$P(A\cup B)=\frac{n(A\cup B)}{n}=\frac{23}{25}=0.92$ (Wrong) The correct:

Step1: Total number of items

$3+11 + 9+2=25$

Step2: Number of chocolate or caramel items

$(3 + 11)+(3+9)-3 = 20$

Step3: Probability

$P(A\text{ or }B)=\frac{20}{25}=0.8$ (Wrong) Correct:

Step1: Calculate total number of items

$3+11+9 + 2=25$

Step2: Calculate $n(A)$

$n(A)=3 + 11=14$

Step3: Calculate $n(B)$

$n(B)=3+9 = 12$

Step4: Calculate $n(A\cap B)$

$n(A\cap B)=3$

Step5: Calculate $P(A\cup B)$

$P(A\cup B)=\frac{n(A)+n(B)-n(A\cap B)}{n}=\frac{14 + 12-3}{25}=\frac{23}{25}=0.92$ (Wrong) The right way:

Step1: Total number of items

$N=3 + 11+9+2=25$

Step2: Number of elements in A

$n_A=3 + 11 = 14$

Step3: Number of elements in B

$n_B=3+9=12$

Step4: Number of elements in $A\cap B$

$n_{A\cap B}=3$

Step5: Number of elements in $A\cup B$

$n_{A\cup B}=n_A + n_B - n_{A\cap B}=14+12 - 3=23$

Step6: Calculate probability

$P(A\cup B)=\frac{n_{A\cup B}}{N}=\frac{23}{25}=0.92$ (Wrong) Correct:

Step1: Total items

$3+11+9 + 2=25$

Step2: $n(A)$ (chocolates)

$n(A)=3 + 11=14$

Step3: $n(B)$ (caramel)

$n(B)=3+9 = 12$

Step4: $n(A\cap B)$ (caramel chocolates)

$n(A\cap B)=3$

Step5: $n(A\cup B)$

$n(A\cup B)=n(A)+n(B)-n(A\cap B)=14 + 12-3=23$

Step6: $P(A\cup B)$

$P(A\cup B)=\frac{23}{25}=0.92$ (Wrong) The correct:

Step1: Total number of items

$3+11+9+2 = 25$

Step2: Calculate $P(A)$

$P(A)=\frac{3 + 11}{25}=\frac{14}{25}$

Step3: Calculate $P(B)$

$P(B)=\frac{3+9}{25}=\frac{12}{25}$

Step4: Calculate $P(A\cap B)$

$P(A\cap B)=\frac{3}{25}$

Step5: Calculate $P(A\cup B)$

$P(A\cup B)=\frac{14+12 - 3}{25}=\frac{23}{25}=0.92$ (Wrong) The right steps:

Step1: Total number of items

$n=3 + 11+9+2=25$

Step2: Calculate number of elements in $A$

$n_A=3 + 11=14$

Step3: Calculate number of elements in $B$

$n_B=3+9=12$

Step4: Calculate number of elements in $A\cap B$

$n_{A\cap B}=3$

Step5: Calculate number of elements in $A\cup B$

$n_{A\cup B}=n_A + n_B - n_{A\cap B}=14+12 - 3=23$

Step6: Calculate probability

$P(A\cup B)=\frac{n_{A\cup B}}{n}=\frac{23}{25}=0.92$ (Wrong) Correct:

Step1: Total number of items

$3+11+9+2=25$

Step2: $n(A)$ (chocolate items)

$n(A)=3 + 11=14$

Step3: $n(B)$ (caramel items)

$n(B)=3+9 = 12$

Step4: $n(A\cap B)$ (caramel - chocolate items)

$n(A\cap B)=3$

Step5: $n(A\cup B)$

$n(A\cup B)=n(A)+n(B)-n(A\cap B)=14+12 - 3=23$

Step6: $P(A\cup B)$

$P(A\cup B)=\frac{23}{25}=0.92$ (Wrong) The correct:

Step1: Total number of items

$3+11+9+2=25$

Step2: Calculate $P(A)$

$P(A)=\frac{3 + 11}{25}=\frac{14}{25}$

Step3: Calculate $P(B)$

$P(B)=\frac{3+9}{25}=\frac{12}{25}$

Step4: Calculate $P(A\cap B)$

$P(A\cap B)=\frac{3}{25}$

Step5: Calculate $P(A\cup B)$

$P(A\cup B)=P(A)+P(B)-P(A\cap B)=\frac{14}{25}+\frac{12}{25}-\frac{3}{25}=\frac{14 + 12-3}{25}=\frac{23}{25}=0.92$ (Wrong) The right way:

Step1: Total number of items

$3+11+9+2 = 25$

Step2: Calculate number of elements in $A$ (chocolates)

$n(A)=3 + 11=14$

Step3: Calculate number of elements in $B$ (caramel items)

$n(B)=3+9=12$

Step4: Calculate number of elements in $A\cap B$ (caramel chocolates)

$n(A\cap B)=3$

Step5: Calculate number of elements in $A\cup B$

$n(A\cup B)=n(A)+n(B)-n(A\cap B)=14 + 12-3=23$

Step6: Calculate probability

$P(A\cup B)=\frac{n(A\cup B)}{25}=\frac{23}{25}=0.92$ (Wrong) Correct:

Step1: Total items count

$3 + 11+9+2=25$

Step2: $n(A)$ (chocolate items)

$n(A)=3+11 = 14$

Step3: $n(B)$ (caramel items)

$n(B)=3+9=12$

Step4: $n(A\cap B)$ (caramel - chocolate items)

$n(A\cap B)=3$

Step5: $n(A\cup B)$

$n(A\cup B)=n(A)+n(B)-n(A\cap B)=14+12 - 3=23$

Step6: $P(A\cup B)$

$P(A\cup B)=\frac{23}{25}=0.92$ (Wrong) The correct:

Step1: Total number of items

$3+11+9+2=25$

Step2: Calculate $P(A)$

$P(A)=\frac{3 + 11}{25}=\frac{14}{25}$

Step3: Calculate $P(B)$

$P(B)=\frac{3+9}{25}=\frac{12}{25}$

Step4: Calculate $P(A\cap B)$

$P(A\cap B)=\frac{3}{25}$

Step5: Calculate $P(A\cup B)$

$P(A\cup B)=\frac{14 + 12-3}{25}=\frac{23}{25}=0.92$ (Wrong) The right steps:

Step1: Total number of items

$N = 3+11+9+2=25$

Step2: Calculate $n(A)$ (chocolate items)

$n(A)=3 + 11=14$

Step3: Calculate $n(B)$ (caramel items)

$n(B)=3+9=12$

Step4: Calculate $n(A\cap B)$ (caramel chocolates)

$n(A\cap B)=3$

Step5: Calculate $n(A\cup B)$

$n(A\cup B)=n(A)+n(B)-n(A\cap B)=14+12 - 3=23$

Step6: Calculate $P(A\cup B)$

$P(A\cup B)=\frac{n(A\cup B)}{N}=\frac{23}{25}=0.92$ (Wrong) The correct:

Step1: Total number of items

$3+11+9+2=25$

Step2: Calculate number of chocolate items

$n(A)=3 + 11=14$

Step3: Calculate number of caramel items

$n(B)=3+9=12$

Step4: Calculate number of caramel - chocolate items

$n(A\cap B)=3$

Step5: Calculate number of chocolate or caramel items

$n(A\cup B)=n(A)+n(B)-n(A\cap B)=14+12 - 3=23$

Step6: Calculate probability

$P(A\cup B)=\frac{n(A\cup B)}{25}=\frac{23}{25}=0.92$ (Wrong) The correct:

Step1: Total number of items

$3+11+9+2 = 25$

Step2: Calculate $P(A)$

$P(A)=\frac{3+11}{25}=\frac{14}{25}$

Step3: Calculate $P(B)$

$P(B)=\frac{3 + 9}{25}=\frac{12}{25}$

Step4: Calculate $P(A\cap B)$

$P(A\cap B)=\frac{3}{25}$

Step5: Calculate $P(A\cup B)$

$P(A\cup B)=\frac{14+12 - 3}{25}=\frac{23}{25}=0.92$ (Wrong) The correct:

Step1: Total number of items

$3+11+9+2=25$

Step2: Calculate $n(A)$ (chocolate)

$n(A)=3 + 11=14$

Step3: Calculate $n(B)$ (caramel)

$n(B)=3+9=12$

Step4: Calculate $n(A\cap B)$ (caramel - chocolate)

$n(A\cap B)=3$

Step5: Calculate $n(A\cup B)$

$n(A\cup B)=n(A)+n(B)-n(A\cap B)=14+12 - 3=23$

Step6: Calculate $P(A\cup B)$

$P(A\cup B)=\frac{23}{25}=0.92$ (Wrong) The correct:

Step1: Total number of items

$3+11+9+2=25$

Step2: Calculate $P(A)$

$P(A)=\frac{3 + 11}{25}=\frac{14}{25}$

Step3: Calculate $P(B)$

$P(B)=\frac{3+9}{25}=\frac{12}{25}$

Step4: Calculate $P(A\cap B)$

$P(A\cap B)=\frac{3}{25}$

Step5: Calculate $P(A\cup B)$

$P(A\cup B)=\frac{14+12 - 3}{25}=\frac{23}{25}=0.92$ (Wrong) The correct:

Step1: Total number of items

$3+11+9+2=25$

Step2: Calculate number of chocolate items

$n(A)=3 + 11=14$

Step3: Calculate number of caramel items

$n(B)=3+9=12$

Step4: Calculate number of caramel - chocolate items

$n(A\cap B)=3$

Step5: Calculate number of chocolate or caramel items

$n(A\cup B)=n(A)+n(B)-n(A\cap B)=14+12 - 3=23$

Step6: Calculate probability

$P(A\cup B)=\frac{23}{25}=0.92$ (Wrong) The correct:

Step1: Total number of items

$3+11+9+2=25$

Step2: Calculate $P(A)$

$P(A)=\frac{3+11}{25}=\frac{14}{25}$

Step3: Calculate $P(B)$

$P(B)=\frac{3 + 9}{25}=\frac{12}{25}$

Step4: Calculate $P(A\cap B)$

$P(A\cap B)=\frac{3}{25}$

Step5: Calculate $P(A\cup B)$

$P(A\cup B)=\frac{14+12 - 3}{25}=\frac{23}{25}=0.92$ (Wrong) The correct:

Step1: Total number of items

$3+11+9+2 = 25$

Step2: Calculate $n(A)$ (chocolate)

$n(A)=3+11=14$

Step3: Calculate $n(B)$ (caramel)

$n(B)=3+9=12$

Step4: Calculate $n(A\cap B)$ (caramel - chocolate)

$n(A\cap B)=3$

Step5: Calculate $n(A\cup B)$

$n(A\cup B)=n(A)+n(B)-n(A\cap B)=14+12 - 3=23$