To find the probability that the first two questions will go to girls, we can follow these steps:
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Total students in the class: There are 8 boys and 16 girls, giving us a total of 8 + 16 = 24 students.
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Probability that the first question goes to a girl: \[ P(\text{first question to a girl}) = \frac{\text{number of girls}}{\text{total students}} = \frac{16}{24} = \frac{2}{3} \]
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Probability that the second question goes to a girl following the first: If the first question went to a girl, then there are now 15 girls left out of a total of 23 students (since one girl was already selected). \[ P(\text{second question to a girl}) = \frac{\text{number of girls left}}{\text{total students left}} = \frac{15}{23} \]
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Combined probability: The probability of both events happening (first and second questions going to girls) is: \[ P(\text{both questions to girls}) = P(\text{first question to a girl}) \times P(\text{second question to a girl}) = \frac{16}{24} \times \frac{15}{23} = \frac{2}{3} \times \frac{15}{23} = \frac{30}{69} = \frac{10}{23} \]
Thus, the probability that the first two questions will go to girls is: \[ \frac{10}{23} \]
The correct response is 10 over 23.