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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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