at a school picnic, students may choose bananas, strawberries, or grapes for a snack, and they may choose…

at a school picnic, students may choose bananas, strawberries, or grapes for a snack, and they may choose water, iced tea, or lemonade to drink. kelly randomly chooses a fruit and a drink. what is the probability that kelly will choose a banana or water but not both? show your work.

at a school picnic, students may choose bananas, strawberries, or grapes for a snack, and they may choose water, iced tea, or lemonade to drink. kelly randomly chooses a fruit and a drink. what is the probability that kelly will choose a banana or water but not both? show your work.

Answer

Explanation:

Step1: Calculate total combinations

There are 3 fruits and 3 drinks. So the total number of combinations of choosing a fruit - drink pair is $3\times3 = 9$.

Step2: Calculate number of favorable cases

Case 1: Choose a banana but not water. There are 2 non - water drinks when choosing a banana, so 2 cases. Case 2: Choose water but not a banana. There are 2 non - banana fruits when choosing water, so 2 cases. The total number of favorable cases is $2 + 2=4$.

Step3: Calculate probability

The probability $P$ is the number of favorable cases divided by the total number of cases. So $P=\frac{4}{9}$.

Answer:

$\frac{4}{9}$