Question

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.

Explanation:

Step1: Calculate total number of items

$3 + 11+9 + 2=25$

Step2: Calculate P(A)

Number of chocolates is $3 + 11=14$, so $P(A)=\frac{14}{25}$

Step3: Calculate P(B)

Number of caramel - items is $3 + 9=12$, so $P(B)=\frac{12}{25}$

Step4: Calculate P(A and B)

Number of caramel - chocolates is 3, so $P(A\ and\ B)=\frac{3}{25}$

Step5: Calculate P(A or B)

Using the formula $P(A\ or\ B)=P(A)+P(B)-P(A\ and\ B)$, we have $P(A\ or\ B)=\frac{14}{25}+\frac{12}{25}-\frac{3}{25}=\frac{14 + 12-3}{25}=\frac{23}{25}=0.92$

Answer:

$0.92$