If A speaks the truth 80% of the times, B speaks the truth 60% of the times.…
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If A speaks the truth 80% of the times, B speaks the truth 60% of the times. What is the probability that they tell the truth at the same time ?
- A.
0.8
- B.
0.48
- C.
0.6
- D.
0.14
Attempted by 86 students.
Show answer & explanation
Correct answer: B
Key idea: If A and B act independently, the probability both tell the truth at the same time equals P(A tells truth) × P(B tells truth).
Convert percentages to decimals: P(A) = 80% = 0.8, P(B) = 60% = 0.6.
Multiply the probabilities: 0.8 × 0.6 = 0.48.
Optional fraction form: (4/5) × (3/5) = 12/25 = 0.48.
Final answer: 0.48
Note: Do not describe these events as mutually exclusive — mutually exclusive events cannot occur together. Here the events (A tells the truth) and (B tells the truth) are independent, so we multiply their probabilities.