Question
A class has 16 boys and 10 girls. Two learners are to be chosen one after the other to represent the school in a competition. Calculate the probability that the learners chosen are both of the same sex
Answers
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To calculate the probability that the learners chosen are both of the same sex, we need to consider two cases: both learners are boys, or both learners are girls.
The probability of choosing a boy as the first learner is 16 boys / (16 boys + 10 girls) = 16/26 = 8/13.
After the first learner is chosen, there will be 15 boys left out of 25 remaining learners. So, the probability of choosing a boy as the second learner, given that the first learner was a boy, is 15 boys / 25 learners = 3/5.
Thus, the probability of choosing two boys in a row is (8/13) * (3/5) = 24/65.
Similarly, the probability of choosing a girl as the first learner is 10 girls / (16 boys + 10 girls) = 10/26 = 5/13.
After the first learner is chosen, there will be 9 girls left out of 25 remaining learners. So, the probability of choosing a girl as the second learner, given that the first learner was a girl, is 9 girls / 25 learners = 9/25.
Thus, the probability of choosing two girls in a row is (5/13) * (9/25) = 45/325.
Therefore, the probability that the learners chosen are both of the same sex is (24/65) + (45/325) = 156/325 ≈ 0.48 or 48%.
The probability of choosing a boy as the first learner is 16 boys / (16 boys + 10 girls) = 16/26 = 8/13.
After the first learner is chosen, there will be 15 boys left out of 25 remaining learners. So, the probability of choosing a boy as the second learner, given that the first learner was a boy, is 15 boys / 25 learners = 3/5.
Thus, the probability of choosing two boys in a row is (8/13) * (3/5) = 24/65.
Similarly, the probability of choosing a girl as the first learner is 10 girls / (16 boys + 10 girls) = 10/26 = 5/13.
After the first learner is chosen, there will be 9 girls left out of 25 remaining learners. So, the probability of choosing a girl as the second learner, given that the first learner was a girl, is 9 girls / 25 learners = 9/25.
Thus, the probability of choosing two girls in a row is (5/13) * (9/25) = 45/325.
Therefore, the probability that the learners chosen are both of the same sex is (24/65) + (45/325) = 156/325 ≈ 0.48 or 48%.