The event of picking the first sock affects the probability of picking the second sock. Thus, the events are dependent.
92/287
Practice makes perfect
The event of picking the first sock affects the probability of picking the second sock. This is because there is one fewer sock to pick. 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 picking a black sock. In a laundry basket there are 42 socks and 24 of them are black.
P(A)&=24/42 l←black socks ←all socks
Here, P(B|A) is the probability of picking another black sock, given that the first picked sock is black. Because we already picked one sock, there are 41 socks left and out of these we have 23 black ones.
P(B|A)&= 23/41 l←remainingblack socks ←remainingsocks
Finally, according to the formula, to calculate P(AandB) we have to multiply P(A) and P(B|A).
