Problem Analysis:

Let’s calculate the probabilities step by step:

1. Class Composition:

   • 70% of the class are boys.
   • 30% of the class are girls.

2. Irregular Attendance:

   • 5% of boys are irregular.
   • 3% of girls are irregular.

3. Regular Attendance:

   • Regular boys: $100\% - 5\% = 95\%$.
   • Regular girls: $100\% - 3\% = 97\%$.

Probability Calculations

1. Probability of a randomly selected student being regular:

Let’s assume the total number of students in the class is $N$ (this cancels out in probabilities, so it’s not needed explicitly). We calculate the regular student proportion:

• Regular boys:
  $P(\text{Regular Boys}) = 0.7 \times 0.95 = 0.665$.

• Regular girls:
  $P(\text{Regular Girls}) = 0.3 \times 0.97 = 0.291$.

Total Probability of Regular Students: $P(\text{Regular}) = P(\text{Regular Boys}) + P(\text{Regular Girls}) = 0.665 + 0.291 = 0.956.$

2. Probability that an irregular student is a girl:

Let’s calculate the total proportion of irregular students first:

• Irregular boys:
  $P(\text{Irregular Boys}) = 0.7 \times 0.05 = 0.035$.

• Irregular girls:
  $P(\text{Irregular Girls}) = 0.3 \times 0.03 = 0.009$.

Total Probability of Irregular Students: $P(\text{Irregular}) = 0.035 + 0.009 = 0.044.$

Now, the probability that an irregular student is a girl is: P(\text{Girl | Irregular}) = \frac{P(\text{Irregular Girls})}{P(\text{Irregular})} = \frac{0.009}{0.044} \approx 0.2045 \, (\text{20.45%}).

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Final Answers:

1. Probability of selecting a regular student: P(\text{Regular}) = 0.956 \, (\text{95.6%}).

2. Probability that an irregular student is a girl: P(\text{Girl | Irregular}) \approx 0.2045 \, (\text{20.45%}).

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Would you like a step-by-step breakdown or clarification on any part of the calculation?

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Related Questions:

1. How would the probabilities change if the percentage of boys and girls were equal?
2. What is the probability that a randomly selected boy is regular?
3. If there are 100 students, how many boys and girls are regular?
4. How does increasing the irregularity percentage for girls affect $P(\text{Regular})$?
5. How can this problem be modeled using a tree diagram?

Tip:

Always double-check probabilities sum to 1 when solving problems involving complementary events like regularity and irregularity.