Question

an item is randomly drawn from a bag with 16 fruit cups, 3 vegetable cups, 14 fruit cans, and 7 vegetable cans. event a: vegetable event b: cup 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

$16 + 3+14 + 7=40$

Step2: Calculate P(A)

Number of vegetable items is $3 + 7 = 10$. So $P(A)=\frac{10}{40}$

Step3: Calculate P(B)

Number of cup - items is $16+3 = 19$. So $P(B)=\frac{19}{40}$

Step4: Calculate P(A and B)

Number of vegetable cups is 3. So $P(A\ and\ B)=\frac{3}{40}$

Step5: Calculate P(A or B)

Using the formula $P(A\ or\ B)=P(A)+P(B)-P(A\ and\ B)$, we have $P(A\ or\ B)=\frac{10}{40}+\frac{19}{40}-\frac{3}{40}=\frac{10 + 19-3}{40}=\frac{26}{40}=0.65$

Answer:

$0.65$