Multiple choice

Peter has ten coloured cubes in a bag. Three of the cubes are red and seven are blue. He draws a cube at random from the bag and notes the colour. Then, without replacement, he randomly draws another cube. What is the probability that he selected a red cube after a blue cube?

  1. 0.233

  2. 0.249

  3. 0.264

  4. 0.278
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A Correct answer
Explanation

Total cubes = 10. Blue = 7, Red = 3. P(Blue first) = 7/10. Remaining cubes = 9. P(Red second | Blue first) = 3/9 = 1/3. Total probability = (7/10) * (1/3) = 7/30 = 0.2333...

AI explanation

Using the multiplication rule for dependent events, multiply the probability of drawing a blue cube first by the probability of drawing a red cube second. The first probability is 7/10, and since the draw is without replacement, the second probability is 3/9. Multiplying these gives 21/90, which equals 0.233.

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