The event of selecting the first student affects the probability of selecting the second one. Thus, the events are dependent.
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Practice makes perfect
The event of selecting the first student affects the probability of selecting the second one. This is because there is one fewer student from which we select. Therefore, the events are dependent.
Probability of Dependent Events
If two events A and B are dependent, then the probability that A and B will occur is
P(AandB)=P(A)* P(B|A)
Let's start by calculating the probability of selecting a student with hazel eyes. In Mrs. Ameldo's class there are 20 students and 7 of them have brown eyes.
P(A)&=7/20 l←students with brown eyes ←all students
Here, P(B|A) is the probability of selecting a student with blue eyes, given that the first selected student has brown eyes. Because we already selected one student, there are 19 students left and out of these 5 have blue eyes.
P(B|A)&= 5/19 l←students with blue eyes ←remainingstudents
Finally, according to the formula, to calculate P(AandB) we have to multiply P(A) and P(B|A).
