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Question
A class consists of 10 boys and 8 girls. Three students are selected at random. What is the probability that the selected group has at least one girl?
Solution
Total number of students = (10 + 8) = 18
Let S be the sample space.
Then n(S) = number of ways of selecting 3 students out of 18 = 18C3 ways
Probability of at least one girl = 1 - P(no girl)
= 1 - P(all 3 are boys)
=\[1 - \frac{^{10}{}{C}_3}{^{18}{}{C}_3} = 1 - \frac{5}{34} = \frac{29}{34}\]
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