Answer :
Answer:
0.4054 = 40.54% probability of selecting a black sock on the second draw given that a black sock was selected on the first draw
Step-by-step explanation:
Conditional Probability
We use the conditional probability formula to solve this question. It is
[tex]P(B|A) = \frac{P(A \cap B)}{P(A)}[/tex]
In which
P(B|A) is the probability of event B happening, given that A happened.
[tex]P(A \cap B)[/tex] is the probability of both A and B happening.
P(A) is the probability of A happening.
In this question:
Event A: Black sock on the first draw.
Event B: Black sock on the second draw.
The probability of selecting a black sock on the first draw is 8/19.
This means that [tex]P(A) = \frac{8}{19}[/tex]
Black socks on both draws:
The probability of selecting two black socks is 120/703
This means that [tex]P(A \cap B) = \frac{120}{703}[/tex]
What is the probability of selecting a black sock on the second draw given that a black sock was selected on the first draw?
[tex]P(B|A) = \frac{P(A \cap B)}{P(A)}[/tex]
[tex]P(B|A) = \frac{\frac{120}{703}}{\frac{8}{19}}[/tex]
[tex]P(B|A) = \frac{120}{703}*\frac{19}{8}[/tex]
[tex]P(B|A) = \frac{120*19}{703*8}[/tex]
[tex]P(B|A) = 0.4054[/tex]
0.4054 = 40.54% probability of selecting a black sock on the second draw given that a black sock was selected on the first draw