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) → \(\frac{27}{50}\)
A and B say the same thing about an event in two ways: both tell the truth, or both lie. The two speak independently, so each case is the product of their separate probabilities, and the two cases are added.
A tells the truth: 0.7, so A lies: 0.3
B lies: 0.4, so B tells the truth: 0.6
Both tell the truth: \(0.7\times0.6=0.42\)
Both lie: \(0.3\times0.4=0.12\)
Same statement: \(\displaystyle 0.42+0.12=0.54=\frac{27}{50}\)
Tip: The question gives B’s chance of lying, not of telling the truth. Using 0.4 as B’s truth gives \(0.7\times0.4+0.3\times0.6=0.46=\frac{23}{50}\), which is Option (1).