There are 10 girls and six boys in a class. The teacher randomly jobs one of the students name and then draws another. What is the probability that the first name John will be a boy in the second will be a girl
20%
I think you must mean "randomly draws" and "first name drawn"
I guess your diction needs some work ...
anyway, 6/16 * 10/15
To find the probability, we first need to determine the total number of possibilities.
The first name can be from any student in the class, so there are 16 possible choices.
If the first name drawn is John (a boy), then there are 6 boys left and 10 girls remaining. Therefore, the probability of the first name being a boy (John) is 6/16.
If we assume that the first name drawn is indeed John (since the question asks for this), then for the second name to be a girl, there will be 10 girls remaining out of the remaining 15 students in the class. Therefore, the probability of the second name being a girl is 10/15.
To find the joint probability of both events occurring (first name being a boy and the second name being a girl), we multiply the individual probabilities:
(6/16) x (10/15)
Simplifying this expression gives us a probability of 2/8 or 1/4, which can be further simplified to 0.25 or 25%. Thus, the probability that the first name drawn is John (a boy) and the second name drawn is a girl is 25%.