Question

Below is the probability tree representing natalie selecting socks.

What is the probability that Natalie selects at least one black sock?

Answer 1

`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)`