In a group activity class, there are 10 students whose ages are 16, 17, 15,
14, 19, 17, 16, 19, 16 and 15 years. One student is selected at random
such that each has equal chance of being chosen and age of the student is
recorded.
On the basis of the above information, answer the following questions :
Question: 1
Find the probability that the age of the selected student is a composite number.
Question:
The ages (in years) of 10 students in a group are:
14, 15, 15, 16, 16, 16, 17, 17, 19, 19.
If a student is selected at random, find the probability that the student’s age is a composite number.
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Question: 2
Let X be the age of the selected student. What can be the value of X ?
Step 1: Extract ages greater than 15:
\[
\text{Ages }>15 = \{16, 17, 17, 16, 19, 16, 19\}
\]
Total count = 7 students.
Step 2: Identify which of these are prime numbers:
Prime ages in the list = 17, 19
17 occurs 2 times, 19 occurs 2 times ⇒ Total prime occurrences = 4
Step 3: Use conditional probability:
\[
P(\text{prime} \mid \text{age}>15) = \frac{\text{Number of prime ages>15}}{\text{Total number of ages>15}} = \frac{4}{7}
\]
Final Answer:
\( \boxed{\dfrac{4}{7}} \)