Question

A drawer contains several white (W), Purple (P), and Black (B) socks. Two socks are selected in the dark without replacement. Construct a tree diagram, list all the possible outcomes. a) How many outcomes are possible? b) How many outcomes match the event: two socks are the same colon" c) What is the probability of reaching into the drawer in the dark and pulling out two socks that are the same color?

Answer 1

First, we need to do the Tree Diagram

WW

W WP

WB

PW

Socks P PP

PB

BW

B BP

BB

a)

As we can see in the Tree Diagram we have 9 outcomes possible.

b)

Same color event (WW,PP, BB), we have 3 possible outcomes

c)

we have in total 9 events

the probability that the outcome

$P(same\text{ color)}=\frac{3}{12}$