a birthday party caterer counted the number of juice cups on the table. the cups contained different…

a birthday party caterer counted the number of juice cups on the table. the cups contained different flavored juices and different shaped straws. heart - shaped straw star - shaped straw orange juice 8 10 grape juice 4 15 pineapple juice 8 4 what is the probability that a randomly selected cup contains pineapple juice or does not contain a star - shaped straw? simplify any fractions.

a birthday party caterer counted the number of juice cups on the table. the cups contained different flavored juices and different shaped straws. heart - shaped straw star - shaped straw orange juice 8 10 grape juice 4 15 pineapple juice 8 4 what is the probability that a randomly selected cup contains pineapple juice or does not contain a star - shaped straw? simplify any fractions.

Answer

Explanation:

Step1: Calculate total number of cups

$8 + 10+4 + 15+8 + 4=49$

Step2: Calculate number of cups with pineapple juice

$8 + 4=12$

Step3: Calculate number of cups without star - shaped straw

$8 + 4+8 = 20$

Step4: Calculate number of cups with pineapple juice and without star - shaped straw

$8$

Step5: Use the inclusion - exclusion principle

$P(A\cup B)=P(A)+P(B)-P(A\cap B)$ Number of cups in $A\cup B=(12 + 20-8)=24$ Probability $=\frac{24}{49}$

Answer:

$\frac{24}{49}$