Probability
Probability
Allen Star Batch
Grade 12
Question:
$A$ speaks truth in 60% cases and $B$ speaks truth in 70% cases. The probability that they will say the same thing while describing single event is:
$0.56$
$0.54$
$0.38$
$0.94$
Step-by-Step Solution
Key Concept: Agreement occurs through two mutually exclusive complementary events: both truthful or both lying.
Two people say the same thing when either both speak truth or both lie. The probability is $(0.6 imes 0.7) + (1 - 0.6)(1 - 0.7) = 0.42 + 0.12 = 0.54$.
Correct Answer: 2