Probability Geometry

Question

A sock drawer has 8 black socks, 7 white socks, and 4 striped socks. Timber will randomly pull out 2 socks without looking in the drawer. Which answer choice describes an event that is not certain in this context?

The Sock Drawer

All combinations of two socks with at least one white sock

All combinations of two socks

4 black socks

Answer 1

A sock drawer has 8 black socks, 7 white socks, and 4 striped socks. Timber will randomly pull out 2 socks without looking in the drawer. Which answer choice describes an event that is not certain in this context?

All combinations of two socks with at least one white sock

Timber may pick BW, WW, or WS.

Each of these events has a probability 0 ≤ P ≤ 1.

All combinations of two socks

Timber may pick BB, BW, BS, WW, WS, or SS.

Each of these events has a probability 0 ≤ P ≤ 1.

4 black socks

This is one event [pick 4 black socks]

Since Timber picks just 2 socks, it is impossible [that is, P=0] for this event to happen. It is not certain. And it is certainly not going to happen.

Answer 2

TImber MUST select THREE (3) socks per the pigeon-hole argument in order to get a GUARANTEED match.

The following events are NOT certain:

2 black

2 white

2 striped

1 black and 1 white

1 black and 1 striped

1 white and 1 striped