A speaks the truth in 70% of cases and B lies in 40% of cases. The probability that they will say the same thing while describing a single event (to have occurred or not) will be:
Answer & explanation
Correct answer: option 4
The correct answer is Option (4) → $\frac{27}{50}$
Step 1: Define probabilities
- A speaks truth 70% of the time → $P(A\text{ truth}) = 0.7, P(A\text{ lie}) = 0.3$
- B lies 40% of the time → $P(B\text{ lie}) = 0.4,P(B\text{ truth}) = 0.6$
We are asked: probability that they say the same thing.
Step 2: Cases where they say the same thing
- Both tell the truth → probability = $0.7 \times 0.6 = 0.42$
- Both lie → probability = $0.3 \times 0.4 = 0.12$
Step 3: Add probabilities
$P(\text{same thing}) = 0.42 + 0.12 = 0.54$
Step 4: Convert to fraction
$0.54 = \frac{54}{100} = \frac{27}{50}$