CMA Foundation · Fundamentals of Business Mathematics and Statistics · Probability
A box has 5 red and 3 blue pens. Two pens are drawn one by one without replacement. Given that the second pen is blue, what is the probability that the first pen was red?
The probability is 5/7. The chance of red then blue is 15/56 and of blue then blue is 6/56, so the second pen is blue with probability 21/56. Dividing 15/56 by 21/56 gives 5/7.
- A15/56
- B3/7
- C5/7Correct
- D5/8
Explanation
P(R then B) = 5/8×3/7 = 15/56. P(B then B) = 3/8×2/7 = 6/56. P(second blue) = 21/56 = 3/8. Required = 15/56 ÷ 21/56 = 15/21 = 5/7. The option 15/56 is the joint probability, not the conditional one.
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