Question
Download Solution PDFAtal speaks the truth in 70% of the cases and George speaks the truth in 60% cases. In what percentage of cases are they likely to contradict each other in stating the same fact?
Answer (Detailed Solution Below)
Detailed Solution
Download Solution PDFConcept:
- P(not A) = 1 - P(A).
- Probability of a Compound Event [(A and B) or (B and C)] is calculated as:
P[(A and B) or (B and C)] = [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 in 46% of the cases.
Last updated on Jun 12, 2025
->The NIMCET 2025 provisional answer key is out now. Candidates can log in to the official website to check their responses and submit objections, if any till June 13, 2025.
-> NIMCET exam was conducted on June 8, 2025.
-> NIMCET 2025 admit card was out on June 3, 2025.
-> NIMCET 2025 results will be declared on June 27, 2025. Candidates are advised to keep their login details ready to check their scrores as soon as the result is out.
-> Check NIMCET 2025 previous year papers to know the exam pattern and improve your preparation.