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NDA 2024 Maths · Mathematics · Probability · medium

A bag contains 5 red and 3 green balls. Two balls are drawn at random without replacement. The probability that they are of different colours is

Single correct option

A bag contains 5 red and 3 green balls. Two balls are drawn at random without replacement. The probability that they are of different colours is
  1. A. 1556\frac{15}{56}
  2. B. 1528\frac{15}{28}
  3. C. 1328\frac{13}{28}
  4. D. 37\frac37
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Answer: (B) 1528\frac{15}{28}

Favourable selections: one red and one green, (51)(31)=15\binom51\binom31=15, out of (82)=28\binom82=28 equally likely pairs, giving 1528\frac{15}{28}. Trap: 1556\frac{15}{56} counts only the order red-then-green, 1328\frac{13}{28} is the probability of same colours (complement), and 37\frac37 is the chance of green on the second draw.
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Original question written in the NDA 2024 Maths pattern and checked twice for the correct answer. Not an official question paper. How we write and check questions · Corrections policy · Report a mistake