Below is the probability tree representing natalie selecting socks. What is the probability that Natalie selects at least one black sock?

Question

asked Aug 6, 2022 210k views

1 Answer

Liatz · Answer 1 · 2022-08-10T01:44:32+0000

Answer:

$P(Black \ge 1) = (55)/(64)$

Explanation:

Given

The attached tree diagram

Required

$P(Black \ge 1)$ --- at least 1 black socks

To do this, we consider the following selections of black (b)

$b = \{BB, BW, WB\}$

Where

$B\to Black$

$W\to White$

From the attached tree diagram, we have:

BB =(25)/(64)

BW =(15)/(64)

WB =(15)/(64)

So:

$P(Black \ge 1) = BB + BW + WB$

$P(Black \ge 1) = (25)/(64) + (15)/(64) + (15)/(64)$

Take LCM

$P(Black \ge 1) = (25+15+15)/(64)$

$P(Black \ge 1) = (55)/(64)$