Question:medium

P and Q play chess frequently against each other. Of these matches, P has won 80% of the matches, drawn 15% of the matches, and lost 5% of the matches.
If they play 3 more matches, what is the probability of P winning exactly 2 of these 3 matches?

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When solving binomial probability problems, remember the formula \( P(X = k) = \binom{n}{k} p^k (1-p)^{n-k} \) and carefully calculate the combinations, probabilities, and powers.
Updated On: Nov 25, 2025
  • \( \frac{48}{125} \)
  • \( \frac{16}{125} \)
  • \( \frac{16}{25} \)
  • \( \frac{25}{48} \)

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Questions Asked in GATE AR exam

Identify the option that has the most appropriate sequence such that a coherent paragraph is formed:
Statement:
P. At once, without thinking much, people rushed towards the city in hordes with the sole aim of grabbing as much gold as they could.
Q. However, little did they realize about the impending hardships they would have to face on their way to the city: miles of mud, unfriendly forests, hungry beasts, and inimical local lords—all of which would reduce their chances of getting gold to almost zero.
R. All of them thought that easily they could lay their hands on gold and become wealthy overnight.
S. About a hundred years ago, the news that gold had been discovered in Kolar spread like wildfire and the whole State was in raptures.
 

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