The event of selecting the first blouse affects the probability of selecting the second blouse. Thus, the events are dependent.
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Practice makes perfect
The event of selecting the first blouse affects the probability of selecting the second blouse. This is because there is one fewer blouse 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 black blouse. In Maddie's closet, there are 11 blouses and 4 of them are black.
P(A)&=4/11 l←black blouses ←all blouses
Here, P(B|A) is the probability of selecting a yellow blouse, given that the first selected blouse is black. Because we already picked one blouse, there are 10 blouses left and out of these we have 2 yellow ones.
P(B|A)&= 2/10 l←yellow blouses ←remainingblouses
Finally, according to the formula, to calculate P(AandB) we have to multiply P(A) and P(B|A).
