Answer:
[tex]Probability = 0.4[/tex]
Step-by-step explanation:
Given
[tex]White = 6[/tex]
[tex]Black = 4[/tex]
Required
Probability that second is black
This selection can be represented as:
(Black and Black) or (White and Black)
The probability of Black and Black is:
[tex]P(Black\ Only) = \frac{Black}{Total} * \frac{Black - 1}{Total - 1}[/tex]
1 is subtracted from the second fraction because it is probability without replacement
[tex]P(Black\ Only) = \frac{4}{10} * \frac{4- 1}{10 - 1}[/tex]
[tex]P(Black\ Only) = \frac{4}{10} * \frac{3}{9}[/tex]
[tex]P(Black\ Only) = \frac{2}{5} * \frac{1}{3}[/tex]
[tex]P(Black\ Only) = \frac{2}{15}[/tex]
The probability of White and Black is:
[tex]P(Black\ and\ White) = \frac{Black}{Total} * \frac{White}{Total - 1}[/tex]
1 is subtracted from the second fraction because it is probability without replacement
[tex]P(Black\ and\ White) = \frac{4}{10} * \frac{6}{10- 1}[/tex]
[tex]P(Black\ and\ White) = \frac{4}{10} * \frac{6}{9}[/tex]
[tex]P(Black\ and\ White) = \frac{2}{5} * \frac{2}{3}[/tex]
[tex]P(Black\ and\ White) = \frac{4}{15}[/tex]
So, the required probability is:
[tex]Probability = P(Black\ Only) + P(Black\ and\ White)[/tex]
[tex]Probability = \frac{2}{15} + \frac{4}{15}[/tex]
[tex]Probability = \frac{2+4}{15}[/tex]
[tex]Probability = \frac{6}{15}[/tex]
[tex]Probability = 0.4[/tex]
