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:

$\frac{27}{50}$

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

1. Both tell the truth → probability = $0.7 \times 0.6 = 0.42$
2. 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

$0.54 = \frac{54}{100} = \frac{27}{50}$