Multiple choice

An urn contains 5 red balls and 5 black balls. In the first draw, one ball is picked at random and discarded without noticing its colour. The probability to get a red ball in the second draw is

  1. 1 2

  2. 4 9

  3. 5 9

  4. 6 9

  5. None of these
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A Correct answer
Explanation

This is a classic probability problem. Regardless of the first draw, the probability of drawing a red ball in the second draw remains 5/10 = 1/2 because the first ball's color is unknown.

AI explanation

Using the law of total probability, we account for the two possible scenarios of the discarded card. The probability that a red ball is drawn second equals the probability the first was red multiplied by the chance the second is red, plus the probability the first was black multiplied by the chance the second is red. This calculates to (5/10 times 5/10) + (5/10 times 5/9), which equals 25/100 + 25/90. Adding these fractions gives a total probability of 1/2.

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