Puzzle | Two Sided Coin Flipping

You have two coins, one of which is a regular coin with heads (H) on one side and tails (T) on the other. The second coin, however, has heads on both sides. You randomly pick one coin and flip it, and it lands showing heads (H).

What is the probability that the other side of the coin is also head(H)?

Solution:

The probability that the other side of the coin is also head (H) is 2/3.

Here's the reasoning:

• There are four equally likely outcomes when you randomly choose one of the two coins and flip it:
  • Regular Coin, Heads (RH)
  • Regular Coin, Tails (RT)
  • Double-Heads Coin, Heads (HH)
  • Double-Heads Coin, Heads (HH)

• Since you see heads after flipping, you've eliminated the "Regular Coin, Tails" outcome (RT).
• You are left with three possible outcomes: RH, HH, HH.
• Out of these three outcomes, two coins has the other side also as heads (HH).

Therefore, the probability that the other side of the coin is also heads (H) is 2/3.