# Answer to Question #11141 in Statistics and Probability for Ke_091

Question #11141

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?

Expert's answer

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.

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.

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