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2 Heads or Tails

© Friederike Hofmann, MATH+

© Friederike Hofmann, MATH+

Author: Jaques Resing (TU Eindhoven)
Project: 4TU.AMI

Challenge

In the coin collection of Santa Clause, you will find a coin from the Republic of Heddonia. If you flip this coin, it shows heads with a probability of 3/4 and tails with a probability of 1/4. The coin collection also contains another coin from the Kingdom of Tailland, which shows tails with a probability of 3/4 and heads with a probability of 1/4.

Santa Clause flips both coins simultaneously; one coin comes up heads and the other one tails.

What is the probability p that the coin that comes up heads is the one from the Republic of Heddonia?

Possible answers:

  1. p ≤ 0.55 holds.
  2.  0.55 < p ≤ 0.60 holds.
  3.  0.60 < p ≤ 0.65 holds.
  4.  0.65 < p ≤ 0.70 holds.
  5.  0.70 < p ≤ 0.75 holds.
  6.  0.75 < p ≤ 0.80 holds.
  7.  0.80 < p ≤ 0.85 holds.
  8.  0.85 < p ≤ 0.90 holds.
  9.  0.90 < p ≤ 0.95 holds.
  10.  0.95 < p holds.