Respuesta :
Answer:
60 percent
Step-by-step explanation:
6 black socks, 4 white socks, 10 socks altogether, 60 percent of the socks are black, so is the chance of picking both black socks
The probability that both socks will be black, when there are 6 black socks and 4 white socks in a drawer is 3/9.
What is chain rule in probability?
For two events A and B, by chain rule, we have:
[tex]P(A \cap B) = P(B)P(A|B) = P(A)P(B|A)[/tex]
where P(A|B) is probability of occurrence of A given that B already occurred.
There are 6 black socks and 4 white socks in a drawer. Let A is the event in which one black sock is taken out from drawer.
As there is total 10 socks in drawer. Thus, the probability of one black sock to be taken out from 6,
[tex]P(A)=\dfrac{6}{10}\\P(A)=\dfrac{3}{5}[/tex]
One sock is taken out without looking, and then a second is taken out. Let the event P(A|B) for the other black socks is taken out, given that first sock which is taken out is black.
As there is 9 socks remain in drawer in which 5 is black socks. Thus,
[tex]P(A|B)=\dfrac{5}{9}[/tex]
From the chain rule, the probability that they both will be black is,
[tex]P(A \cap B) = P(A)P(B|A)\\P(A \cap B) = \dfrac{3}{5}\times\dfrac{5}{9}\\P(A \cap B) = \dfrac{3}{9}[/tex]
Thus, the probability that both socks will be black, when there are 6 black socks and 4 white socks in a drawer is 3/9.
Learn more about chain rule here:
https://brainly.com/question/21081988
