Mr. Rosart selects two students from his class to present their book reports. He places the names of each student in a box and randomly picks one at a time. The class has 14 boys and 12 girls. What is the probability that the second name Mr. Rosart picks is a boy, if the first one is a boy also? Round your answer to the nearest percent.
To find the probability that the second name Mr. Rosart picks is a boy, given that the first one is a boy, we need to determine the number of possible outcomes in which the first student selected is a boy and the second student selected is also a boy.
First, let's consider the total number of students in the class, which is the sum of the number of boys and girls:
Total number of students = number of boys + number of girls = 14 + 12 = 26.
If we assume that the first student selected is a boy, then there are now 13 boys and 12 girls left in the box.
Since Mr. Rosart randomly selects one name at a time, there are 25 students left in the box after the first student is selected.
The probability of selecting a boy as the second student, given that the first student is a boy, can be calculated as:
Probability = (number of favorable outcomes) / (total number of possible outcomes).
In this case, the number of favorable outcomes is the number of boys left in the box after selecting the first boy, which is 13.
The total number of possible outcomes is the number of students left in the box after selecting the first student, which is 25.
Therefore, the probability of selecting a boy as the second student, given that the first student is a boy, is:
Probability = 13 / 25 ≈ 0.52
To convert this probability to a percentage, we multiply it by 100:
Probability ≈ 0.52 * 100 ≈ 52%
So, the probability that the second name Mr. Rosart picks is a boy, given that the first one is a boy, is approximately 52%.