Question

In a certain city, the ratio of men to women is \(5:4\). It is found that \(80\%\) of men and \(90\%\) of women are literate. If a person selected at random is found to be illiterate, then the probability that the person is a man is....

• A. \(\frac{2}{3}\)
• B. \(\frac{5}{7}\)
• C. \(\frac{1}{3}\)
• D. \(\frac{2}{7}\)

Hint:

Apply Bayes theorem with ratio 5:4 and illiteracy rates 20% and 10%.

Answer 1

The Correct Option is B

Step 1: Use a concrete population:
Take 900 people: 500 men and 400 women.

Step 2: Count illiterates:
Illiterate men: $20\% \times 500 = 100$. Illiterate women: $10\% \times 400 = 40$. Total illiterates: 140.

Step 3: Fraction:
Chance that a randomly selected illiterate person is a man $= \frac{100}{140} = \frac57$.

Final Answer:
The probability is 5/7, option (B). \[ \boxed{\frac{5}{7}} \]