Question

1. the vegetable display at a market has exactly 52 peaches and 34 plums. of these, 3 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 non - rotten probabilities

The probability of choosing a non - rotten peach is $P(\text{non - rotten peach})=\frac{52 - 5}{52}=\frac{47}{52}$. The probability of choosing a non - rotten plum is $P(\text{non - rotten plum})=\frac{34 - 4}{34}=\frac{30}{34}$.

Step2: Calculate the probability that none are rotten

The probability that both the peach and the plum are non - rotten is $P(\text{none rotten})=\frac{47}{52}\times\frac{30}{34}=\frac{47\times30}{52\times34}=\frac{1410}{1768}$.

Step3: Calculate the probability that at least one is rotten

The probability that at least one is rotten is $P = 1-\frac{47}{52}\times\frac{30}{34}=1-\frac{1410}{1768}=\frac{1768 - 1410}{1768}=\frac{358}{1768}\approx 0.2025 = 20.25\%$.

Answer:

20.25%