Answer to Question #11141 in Statistics and Probability for Ke_091

Question

The odds that X speaks the truth are 3:2 and the odds that Y speaks the truth are 5:3. In what percentage of the cases are they likely to contradict each other?

Answer 1

The probability for X to say the truth is
pX = 3/(3+2) = 3/5
and the
probability for Y to say the truth is
pY = 5/(5+3) = 5/8

The event A
that "they contradict each other" means that
"X speaks the truth and Y
lies or X lies and Y speaks the truth"
Hence
P(A) = pX*(1-pY) +
(1-pX)*pY
= 3/5 * 3/8 + 2/5 * 5/8
= 9/40 + 10/40
=
19/40
= 0.475

Thus in 47.5% of cases X and Y contradict each
other.