Get the best answers to your questions with the help of IDNLearn.com's experts. Join our community to access reliable and comprehensive responses to your questions from experienced professionals.
Sagot :
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.
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.
We appreciate your participation in this forum. Keep exploring, asking questions, and sharing your insights with the community. Together, we can find the best solutions. Thank you for choosing IDNLearn.com. We’re committed to providing accurate answers, so visit us again soon.