To find the expected age of a randomly chosen student from the class, we need to use the concept of expectation in probability. The expected value (or expectation) of a discrete random variable is calculated as the sum of the possible values each multiplied by their respective probabilities.
Here are the steps to find the expected age:
1. Identify the possible ages and their probabilities:
- Age 3: Probability = 0.5
- Age 4: Probability = 0.4
- Age 5: Probability = 0.1
2. Calculate the expected age using the formula for the expected value:
[tex]\[
\text{Expected Age} = (3 \times 0.5) + (4 \times 0.4) + (5 \times 0.1)
\][/tex]
3. Compute each term:
- [tex]\( 3 \times 0.5 = 1.5 \)[/tex]
- [tex]\( 4 \times 0.4 = 1.6 \)[/tex]
- [tex]\( 5 \times 0.1 = 0.5 \)[/tex]
4. Add the results of these computations:
[tex]\[
\text{Expected Age} = 1.5 + 1.6 + 0.5
\][/tex]
5. Sum up the terms to find the final expected age:
[tex]\[
\text{Expected Age} = 3.6
\][/tex]
Therefore, the expected age of a randomly chosen student from the class is [tex]\( \boxed{3.6} \)[/tex] years.
