Let's solve this probability problem step by step.

The problem states:

• There are 6 apples and 4 oranges in a basket.
• Two fruits are chosen one by one without replacement.
• We need to calculate the probability that both fruits chosen are oranges.

Step-by-Step Solution

1. Determine the Total Number of Fruits:

   • Total fruits = 6 apples + 4 oranges = 10 fruits.

2. Calculate the Probability of Selecting the First Orange:

   • The probability of selecting an orange first = $\frac{\text{Number of oranges}}{\text{Total fruits}} = \frac{4}{10} = \frac{2}{5}$.

3. Calculate the Probability of Selecting the Second Orange:

   • After the first orange is chosen, there are now 3 oranges and 9 fruits left in total.
   • The probability of selecting a second orange = $\frac{3}{9} = \frac{1}{3}$.

4. Multiply the Probabilities:

   • Since these events are sequential (selecting one orange and then another), we multiply the probabilities: $\frac{2}{5} \times \frac{1}{3} = \frac{2}{15}$

Final Answer

The probability that both fruits chosen are oranges is $\frac{2}{15}$.

Answer: D

Would you like further details or have any questions about this solution?

Here are 5 additional questions related to this concept:

1. What is the probability of choosing one apple and one orange?
2. How would the probability change if we replaced the first fruit after selecting it?
3. What is the probability of selecting two apples instead of two oranges?
4. How does the total number of fruits affect the probability calculations?
5. Can this problem be approached using combinatorics instead of sequential probability?

Tip: In probability problems, remember to check if events are independent or dependent, as it affects whether probabilities should be multiplied directly or recalculated for each selection.