2024 RVHS H1 Q9

A fruits company sells mangoes in bags of \(10\). The \(10\) mangoes are randomly chosen from a large supply. The probability that a mango is rotten is \(0.12\).

1. Find the probability that, in a randomly selected bag of mangoes, exactly one mango is rotten.[1]

A bag of mangoes is sold at a discounted price if more than \(2\) mangoes in the bag are rotten.

2. Find the probability that a randomly selected bag of mangoes is sold at the discounted price.[2]

Two bags of mangoes are selected at random.

3. Find the probability that both bags are sold at its original price.[2]

Last Sunday, \(50\) bags of mangoes were sold.

4. Find the probability that fewer than \(3\) of these bags were sold at the discounted price.[2]

The company has a wholesaler subsidiary and sells to fruit sellers in cartons of \(n\) mangoes, where \(n\) is greater than \(10\). Find the least number of mangoes needed to be packed in such cartons so that there is a probability of less than \(0.15\) that no more than \(5\) rotten mangoes are found in a carton.[2]