Question

In a club, a member is either an Indian or a non-Indian who is either a man or a woman. One-third of them are women, two-thirds of them are Indian and three-eighths of the non-Indians are women. What is the probability that a man picked at random is a non-Indian?

• A. 0.2925
• B. 0.2525
• C. 0.2125
• D. 0.3125

Hint:

Using a hypothetical total number (e.g., LCM of denominators 3 and 8 = 24 or 240) makes calculations easier than working with variables.

Answer 1

The Correct Option is D

Step 1: Define Variables:
Let total members = \(T\). Non-Indians = \(1 - \frac{2}{3} = \frac{1}{3}T\). Men = \(1 - \frac{1}{3} = \frac{2}{3}T\). Step 2: Analyze Non-Indians:
Given: 3/8 of Non-Indians are women. \(\text{Non-Indian Women} = \frac{3}{8} \times \frac{1}{3}T = \frac{1}{8}T\). Therefore, Non-Indian Men = Total Non-Indians - Non-Indian Women. \(\text{Non-Indian Men} = \frac{1}{3}T - \frac{1}{8}T = \frac{8-3}{24}T = \frac{5}{24}T\). Step 3: Calculate Probability:
We need \(P(\text{Non-Indian} | \text{Man})\). \[ P = \frac{\text{Number of Non-Indian Men}}{\text{Total Number of Men}} \] \[ P = \frac{\frac{5}{24}T}{\frac{2}{3}T} = \frac{5}{24} \times \frac{3}{2} = \frac{5}{16} \] Step 4: Convert to Decimal:
\(\frac{5}{16} = 0.3125\).