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?
Pr(2B:1b)= 13/(13+12)=13/25
To determine the probability that the second name Mr. Rosart picks is a boy, given that the first one is a boy, we need to consider the number of boys and girls remaining in the class after the first boy is chosen.
Step 1: Calculate the probability of choosing a boy on the first pick:
The probability of picking a boy on the first try is 14 boys divided by the total number of students in the class (14 boys + 12 girls), which is:
P(Boy on first pick) = 14 / (14 + 12) = 14 / 26 = 7 / 13.
Step 2: Calculate the probability of choosing a boy on the second pick after the first boy is already selected:
After the first boy is chosen, there are 13 boys and 12 girls left in the class. The probability of choosing a boy on the second try is 13 boys divided by the remaining total number of students (13 boys + 12 girls), which is:
P(Boy on second pick | Boy on first pick) = 13 / (13 + 12) = 13 / 25.
Therefore, the probability that the second name Mr. Rosart picks is a boy, given that the first one is a boy, is 13/25.
To find the probability that the second name Mr. Rosart picks is a boy, given that the first one is also a boy, we need to determine how many boys and girls are left in the box after the first selection.
The probability of selecting a boy for the first pick is 14/26 (since there are 14 boys and a total of 26 students). After the first boy is selected, there are now 13 boys and 12 girls left in the box.
For the second pick, Mr. Rosart has one less student to choose from and one less boy to choose from. Therefore, the probability of selecting a boy for the second pick is 13/25.
So, the probability that the second name Mr. Rosart picks is a boy, given that the first one is also a boy, is 13/25.