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 strawOrange juice 8 10Grape juice 4 15Pineapple juice 8 4What is the probability that a randomly selected cup contains pineapple juice or does not contain a star-shaped straw?Simplify any fractions.
Question
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 strawOrange juice 8 10Grape juice 4 15Pineapple juice 8 4What is the probability that a randomly selected cup contains pineapple juice or does not contain a star-shaped straw?Simplify any fractions.
Solution
To solve this problem, we first need to find the total number of juice cups. We add up all the numbers in the table:
8 (orange juice with heart-shaped straw) + 10 (orange juice with star-shaped straw) + 4 (grape juice with heart-shaped straw) + 15 (grape juice with star-shaped straw) + 8 (pineapple juice with heart-shaped straw) + 4 (pineapple juice with star-shaped straw) = 49 cups in total.
Next, we find the number of cups that contain pineapple juice or do not contain a star-shaped straw.
The number of cups with pineapple juice is 8 (with heart-shaped straw) + 4 (with star-shaped straw) = 12.
The number of cups without a star-shaped straw is 8 (orange juice with heart-shaped straw) + 4 (grape juice with heart-shaped straw) + 8 (pineapple juice with heart-shaped straw) = 20.
However, we have counted the pineapple juice with heart-shaped straw twice, once for being pineapple juice and once for not having a star-shaped straw. So we subtract these 8 cups from our total.
So, the number of favorable outcomes is 12 (cups with pineapple juice) + 20 (cups without star-shaped straw) - 8 (cups counted twice) = 24.
The probability of selecting a cup that contains pineapple juice or does not contain a star-shaped straw is therefore 24/49.
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