Question

A box of oranges is inspected by examining three randomly selected oranges drawn without replacement. If all three oranges are good, the box is approved for sale; otherwise, it is rejected. Find the probability that a box containing 15 oranges, out of which 12 are good and 3 are bad ones, will be approved for sale.

Answer 1

The probability that a box of 15 oranges with 12 good and 3 bad ones will be approved for sale after randomly drawing three oranges without replacement is approximately 44.5%.

Step-by-step explanation:

The student is tasked with finding the probability that a box containing 15 oranges, with 12 good and 3 bad, will be approved for sale by selecting 3 random oranges without replacement and all being good. To solve this probability question, we use the concept of hypergeometric distribution because we are dealing with draws without replacement from a finite population. The calculation involves the following steps:

• Calculate the probability of drawing the first good orange: 12/15.
• Calculate the probability of drawing the second good orange, given the first was good: 11/14.
• Calculate the probability of drawing the third good orange, given the first two were good: 10/13.

Multiplying these probabilities together gives the direct answer for the probability the box is approved: (12/15) × (11/14) × (10/13).

Performing the multiplication, (12/15) × (11/14) × (10/13) equals approximately 0.445, which means the box has a 44.5% chance of being approved for sale.