### Brain Teasers

# Fifty Fifty... Twenty?

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

-You have 5 coins

-One of the coins is rigged to always land on heads

-You grab one at random

-You flip it twice and it lands on heads both times

What is the probability you picked the rigged one?

-One of the coins is rigged to always land on heads

-You grab one at random

-You flip it twice and it lands on heads both times

What is the probability you picked the rigged one?

### Answer

50%The rigged coin will always land on heads twice, so it has a weight of 1

The normal coins will land on heads twice 1/4th of the time, so they have a weight of 1/4.

1+(1/4)*4=200%

To get a valid percent you divide both sides by 2

1/2+(1/4*4)/2=100%

If you remove the probability of the real coins you get

1/2=50%

Alternate explanation:

Rigged Coin's expected average after 4 flips:

HH

HH

HH

HH

Coin 2's expected average after 4 flips:

HH

HT

TH

TT

Coin 3's expected average after 4 flips:

HH

HT

TH

TT

Coin 4's expected average after 4 flips:

HH

HT

TH

TT

Coin 5's expected average after 4 flips:

HH

HT

TH

TT

If you take all the ones with tails, since we know they didn't happen, then you are left with:

HH - RC

HH - RC

HH - RC

HH - RC

HH - C2

HH - C3

HH - C4

HH - C5

As you can see, half the scenarios above are the rigged coin

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