Answer:
[tex]P(Black \ge 1) = \frac{55}{64}[/tex]
Step-by-step explanation:
Given
The attached tree diagram
Required
[tex]P(Black \ge 1)[/tex] --- at least 1 black socks
To do this, we consider the following selections of black (b)
[tex]b = \{BB, BW, WB\}[/tex]
Where
[tex]B\to Black[/tex]
[tex]W\to White[/tex]
From the attached tree diagram, we have:
[tex]BB =\frac{25}{64}[/tex]
[tex]BW =\frac{15}{64}[/tex]
[tex]WB =\frac{15}{64}[/tex]
So:
[tex]P(Black \ge 1) = BB + BW + WB[/tex]
[tex]P(Black \ge 1) = \frac{25}{64} + \frac{15}{64} + \frac{15}{64}[/tex]
Take LCM
[tex]P(Black \ge 1) = \frac{25+15+15}{64}[/tex]
[tex]P(Black \ge 1) = \frac{55}{64}[/tex]
