Multiple choice

A pack of cards is counted with face downwards. It is found that one card is missing. One card is drawn and is found to be red. Then the ability that the missing card is red.

  1. $\dfrac{25}{51}$
  2. $\dfrac{26}{51}$
  3. $\dfrac{1}{2}$
  4. $\dfrac{25}{52}$
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A Correct answer
Explanation

If the missing card is red, the probability of drawing a red card is 25/51; if it is black, that probability is 26/51. Applying conditional probability gives the probability that the missing card was red as 25/51.

AI explanation

By applying Bayes' theorem, we find the updated probability of the missing card's color given the new evidence. The initial probability of the missing card being red is 26/52, and if a red card is missing, the chance of drawing a red card is 25/51. Since the overall probability of drawing a red card from a full deck is 26/52, the posterior probability is calculated as (26/52 times 25/51) divided by 26/52. This results in the fraction 25/51. The probability that the missing card is red is 25/51.

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