35  Probably True / Probably False

35.1 Introduction

In reasoning tests, some statements are neither absolute facts nor clearly falsehoods, but instead lie in the realm of probability.
These questions check your ability to judge the likelihood of a conclusion given the facts, without assuming outside knowledge.

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35.2 1) Understanding the Terms

• Definitely True (DT): The statement must follow directly from the given facts.
  
• Definitely False (DF): The statement clearly contradicts the facts.
  
• Probably True (PT): The statement is not directly stated but seems reasonable given the facts.
  
• Probably False (PF): The statement is not directly contradicted but is unlikely given the facts.
  
• Data Inadequate (DI): Insufficient information to classify.

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35.3 2) Exam Approach

1. Read the facts carefully.
   
2. Assume them to be 100% correct, even if they contradict real-world knowledge.
   
3. Evaluate each conclusion:
   • If it must be true → DT.
     
   • If it must be false → DF.
     
   • If it seems likely but not certain → PT.
     
   • If it seems unlikely but not impossible → PF.
     
   • If nothing can be said → DI.

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35.4 3) Examples

35.4.1 Example 1

Statement: “All engineers are good at mathematics.”
Conclusions:
1. Rajesh, an engineer, is good at mathematics. → Definitely True
2. Sunita, a mathematician, is an engineer. → Definitely False
3. Ravi, an engineer, is probably good at solving puzzles. → Probably True
4. All mathematicians are engineers. → Definitely False

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35.4.2 Example 2

Statement: “Some cats are black.”
Conclusions:
1. There exists at least one black cat. → Definitely True
2. All cats are black. → Definitely False
3. Some cats are probably white. → Probably True
4. No cats are white. → Probably False

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35.4.3 Example 3

Statement: “The government announced new tax reforms.”
Conclusions:
1. Taxes have been changed by the government. → Definitely True
2. The reforms may affect middle-class families. → Probably True
3. The reforms will not affect farmers. → Probably False
4. Government will reduce petrol prices. → Data Inadequate

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35.5 4) Practice Questions

Classify as DT, DF, PT, PF, or DI:

1. Statement: “All schools in the city have computer labs.”
   • 1. ABC School in the city has a computer lab.
        
   • 2. XYZ School in the city has a swimming pool.
        
   • 3. Most schools in the city are probably modern.
        
   • 4. Some schools outside the city have computer labs.
2. Statement: “Some doctors are researchers.”
   • 1. All doctors are researchers.
        
   • 2. At least one doctor is a researcher.
        
   • 3. Some researchers are doctors.
        
   • 4. All researchers are doctors.
3. Statement: “The train was delayed due to heavy rains.”
   • 1. The train did not arrive on time.
        
   • 2. Rainfall may have been severe.
        
   • 3. Roads in the city must have been waterlogged.
        
   • 4. The train was cancelled.

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35.6 5) Suggested Answers

1. 1. DT, (b) DI, (c) PT, (d) DI
      
2. 1. DF, (b) DT, (c) PT, (d) DF
      
3. 1. DT, (b) PT, (c) PF, (d) DI

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35.7 Summary

• Definitely True / False → directly proven or contradicted.
  
• Probably True / False → likely/unlikely but not certain.
  
• Data Inadequate → when facts are insufficient.
  
• Strategy: Stay within the given statements only, avoid outside assumptions.