Brain Teasers/Counterintuitive Cards

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You have 7 cards: two are red on both sides, two are black on both sides, and three are red/black. You choose a card at random, and one of its sides is red. What is the probability that the other side is also red?

Answer

There are 7 cards.

  • R/R : 2
  • B/B : 2
  • R/B : 3

One card is pulled, and the one side is Red. This means, the card is not B/B. It should be either R/R or R/B. The probability of R/B card having R side up is 0.5. That means, there can be 1.5 card with R side up. So the probability of the other side being red is 2/(2 + 1.5) which is 2/3.5 or 4/7.

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