Final answer:
The probability of Ms.B calling on a girl and then a boy, without repeating students, is about 25.71%.
Step-by-step explanation:
The probability that Ms.B calls on a girl and then a boy to work out a problem is the product of the probability of calling on a girl first and the probability of calling on a boy second, given that a girl has already been called.
Since there are 12 girls and 9 boys in the class, and she will not call on someone more than once, the probability of calling on a girl first is 12/21 (since there are 12 girls out of 21 total students).
Once a girl has been called, there are 20 students left (8 boys and 12 girls).
Therefore, the probability of calling a boy second is 9/20 (since there are still 9 boys but only 20 total students left).
To find the overall probability of Ms.B calling on a girl and then a boy, we multiply these two probabilities:
The probability of a girl and then a boy = (12/21) * (9/20) = 0.2571 or roughly 25.71%.