Question

the vegetable display at a market has exactly 52 peaches and 34 plums. of these, 5 of the peaches are rotten, and 4 of the plums are rotten. you randomly choose a peach and a plum from the display. what is the probability that one of the fruits is rotten?

Explanation:

Step1: Calculate total number of fruits

The total number of peaches is 52 and the total number of plums is 34, so the total number of fruits is $52 + 34=86$.

Step2: Calculate number of non - rotten fruits

The number of non - rotten peaches is $52 - 5=47$ and the number of non - rotten plums is $34 - 4 = 30$. So the number of non - rotten fruits is $47+30 = 77$.

Step3: Calculate probability of getting non - rotten fruits

The probability of getting a non - rotten peach and a non - rotten plum when picking one of each is $\frac{47}{52}\times\frac{30}{34}=\frac{1410}{1768}\approx0.7975$.

Step4: Calculate probability of getting at least one rotten fruit

The probability of getting at least one rotten fruit is $1-\frac{1410}{1768}=\frac{1768 - 1410}{1768}=\frac{358}{1768}\approx0.2025 = 20.25\%$

Answer:

$20.25\%$