UPSC NDA Math Model Paper 1

Concept:

• P(notA)=1−P(A)
• Probability of a Compound Event [(A and B) or (B and C)] is calculated as:
  P[(A‌and‌B)‌or(B‌and‌C)]=[P(A)×P(B)]+[P(C)×P(D)]
  ('and' means ′×′ and 'or' means ′+′ )

Calculation:
Probability of Atal speaking the truth is 70%=0.7
Probability of Atal NOT speaking the truth is 1 - 0.7 = 0.3.
Probability of George speaking the truth is 60% = 0.6.
Probability of George NOT speaking the truth is 1 - 0.6 = 0.4.
They both will contradict each other in the following case:
(Atal speaks the truth AND George does not speak the truth) OR (Atal does not speak the truth AND George speaks the truth).
∴ The required probability is:
[P(Atal speaking the truth) × P(George not speaking the truth)] + [P(Atal not speaking the truth) × P(George speaking the truth)]
= (0.7 × 0.4) + (0.3 × 0.6)
= 0.28 + 0.18
= 0.46.
∴ They both contradict each other in46%of the cases.