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
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%.
To calculate the probability of choosing two learners of the same sex, we need to determine the number of possible outcomes and the number of favorable outcomes.
First, let's calculate the total number of possible outcomes. The first learner can be chosen from a total of 26 (16 boys + 10 girls) learners. After the first learner has been chosen, there will be 25 learners left, so the second learner can be chosen from the remaining 25.
Next, let's calculate the number of favorable outcomes. If we want to choose two learners of the same sex, we have two options: either choosing two boys or choosing two girls.
The number of ways to choose two boys from 16 boys is calculated using the combination formula: C(16, 2) = 16! / (2! * (16-2)!) = 16! / (2! * 14!) = (16 * 15) / (2 * 1) = 120.
Similarly, the number of ways to choose two girls from 10 girls is C(10, 2) = 10! / (2! * (10-2)!) = 10! / (2! * 8!) = (10 * 9) / (2 * 1) = 45.
Therefore, the total number of favorable outcomes is 120 + 45 = 165.
Finally, we can calculate the probability by dividing the number of favorable outcomes by the total number of possible outcomes:
Probability = (Number of favorable outcomes) / (Total number of possible outcomes)
= 165 / (26 * 25)
= 165 / 650
≈ 0.2538
Therefore, the probability that the learners chosen are both of the same sex is approximately 0.2538 or approximately 25.4%.