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To find the expected number of oranges per tree, we calculate the *expected value* \( E(X) \) of the distribution. The formula for the expected value is:

\[
E(X) = \sum (x_i \cdot p_i)
\]

where:
- \( x_i \) is the number of oranges,
- \( p_i \) is the corresponding probability.

Given the values from the table:

\[
E(X) = (25 \times 0.10) + (30 \times 0.40) + (35 \times 0.30) + (40 \times 0.20)
\]

Now let's calculate this:

\[
E(X) = (25 \times 0.10) + (30 \times 0.40) + (35 \times 0.30) + (40 \times 0.20) = 2.5 + 12 + 10.5 + 8
\]

\[
E(X) = 33
\]

Thus, the expected number of oranges per tree is **33**.

Would you like more details on how this is computed? Here are some related questions:

1. What is the significance of the expected value in probability?
2. How would the expected value change if the probabilities were different?
3. Can the expected value ever be higher than the largest observed value?
4. How is the expected value used in decision-making processes?
5. What would happen if some of the probabilities didn’t sum up to 1?

**Tip**: The sum of probabilities in any probability distribution must always equal 1, which ensures the distribution is complete.

A citrus farmer has observed the following distribution for the number of oranges per tree. How many oranges does he expect on the average per tree? Oranges: 25, 30, 35, 40; Probability: 0.10, 0.40, 0.30, 0.20

Calculate the expected number of oranges per tree using the probability distribution provided. Learn how to apply the expected value formula to real-life scenarios in probability. Suitable for Grades 9-12.

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