Question

The odds that A agrees with the truth are 3 : 2 and the odds that B agrees with the truth are 5 : 3. In what percent of cases are they likely to agree with each other on an identical point?

• A. 47.5 %
• B. 37.5 %
• C. 63.5 %
• D. None of these

Hint:

Always express probabilities in fractions before converting them into percentages to minimize calculation errors.

Answer 1

The Correct Option is D

We define the probabilities of A and B agreeing with the truth:
The probability that A agrees with the truth: \[ P(A) = \frac{3}{3+2} = \frac{3}{5} \] The probability that B agrees with the truth: \[ P(B) = \frac{5}{5+3} = \frac{5}{8} \] The probabilities of A and B disagreeing: \[ P(A') = 1 - \frac{3}{5} = \frac{2}{5} \] \[ P(B') = 1 - \frac{5}{8} = \frac{3}{8} \] Now, the probability that A and B agree: \[ P(A \cap B) + P(A' \cap B') = \left( \frac{3}{5} \times \frac{5}{8} \right) + \left( \frac{2}{5} \times \frac{3}{8} \right) \] \[ = \left( \frac{15}{40} \right) + \left( \frac{6}{40} \right) = \frac{21}{40} \] \[ \frac{21}{40} \times 100 = 52.5% \] Since 52.5% is not in the options, the correct answer is None of these.