Question

The probability of selecting a man from a crowd containing 20 men and 33 women is

• A. \(\frac{20}{33}\)
• B. \(\frac{33}{20}\)
• C. \(\frac{20}{53}\)
• D. \(\frac{33}{53}\)

Hint:

For a random selection problem, \[ P(E) = \frac{\text{Favourable Outcomes}} {\text{Total Outcomes}}. \] Always include every member of the group in the denominator.

Answer 1

The Correct Option is C

Concept: According to the classical definition of probability, \[ P(E) = \frac{\text{Number of favourable outcomes}} {\text{Total number of possible outcomes}}. \]

Step 1: Find the total number of people. The crowd contains \[ 20 \] men and \[ 33 \] women. Therefore, \[ \text{Total people} = 20+33 = 53. \]

Step 2: Find the favourable outcomes. The event is selecting a man. Hence, \[ \text{Favourable outcomes} = 20. \]

Step 3: Apply the probability formula. \[ P(\text{Selecting a man}) = \frac{20}{53}. \]

Step 4: Match with the options. The obtained probability is \[ \frac{20}{53}, \] which corresponds to Option (C). Conclusion: \[ \boxed{\frac{20}{53}} \]