### Brain Teasers

# Lights Out

Probability
Probability puzzles require you to weigh all the possibilities and pick the most likely outcome.

While Jimbo was daydreaming and trying to figure out how he could fall asleep during writing class, he gazed up to the ceiling and noticed that there were 12 fluorescent lights in the room, arranged in 3 rows. Each row consisted of 4 lights.

He also noticed that 2 of the lights were out. Boy what a coincidence he thought to himself. They're both in the same row.

If two lights out of the 12 in Jimbo's classroom have failed (this is besides Jimbo who is also in danger of failing), what is the probability that

a) They are both in the same row of 4 lights?

b) They are in different columns (of three lights across)?

c) They are in adjacent columns of 3 lights?

He also noticed that 2 of the lights were out. Boy what a coincidence he thought to himself. They're both in the same row.

If two lights out of the 12 in Jimbo's classroom have failed (this is besides Jimbo who is also in danger of failing), what is the probability that

a) They are both in the same row of 4 lights?

b) They are in different columns (of three lights across)?

c) They are in adjacent columns of 3 lights?

### Answer

a) Pick a row = 3 waysPick 2 out of this row = 4C2=6

Sample space = 12C2 = 66

Probability = 3 x 6 / 66 = 3/11

b) First choose in same column

Pick a column = 4 ways

Pick 2 from this column = 3C2 = 3

P same = 4 x 3 / 66 = 2/11

Probability different columns =

1 - 2/11 = 9/11

c) Pick 2 adjacent columns = 3 ways

Pick 1 light from each column = 3x3 = 9

Prob = 3 x 9 / 66 = 9/22

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