Multiple choice

A bag contains three red balls and two blue balls. We remove successively, and with replacement, two balls and observe their colour. What is the probability of "to extract a red ball and a blue one, without taking into account the order"?

  1. $\dfrac{12}{25}$
  2. $\dfrac{13}{25}$
  3. $\dfrac{12}{23}$

  4. None of these
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A Correct answer
Explanation

Total outcomes = 5 * 5 = 25. Outcomes (Red, Blue) or (Blue, Red) = (3*2) + (2*3) = 12. Probability = 12/25.

AI explanation

The total number of balls in the bag is 5, making the probability of drawing a red ball 3/5 and a blue ball 2/5. Since the balls are drawn successively and with replacement, we use the multiplication theorem for independent events to find the probability of getting one red and one blue ball in any order: 2 * (3/5) * (2/5). Multiplying these values yields 12/25. The probability is 12/25.

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