Question

Ram and Rahim are contesting for two vacancies in a company. Probability of selection of Ram is \( \frac{7}{9} \) and that of Rahim is \( \frac{4}{7} \). What is the probability that both will be selected?

• A. \( \frac{61}{63} \)
• B. \( \frac{4}{9} \)
• C. \( \frac{8}{9} \)
• D. \( \frac{11}{16} \)

Hint:

In probability word problems, the word "and" usually implies multiplication of probabilities, provided the events do not affect each other.

Answer 1

The Correct Option is B

Step 1: Understanding the Concept:
The selection of Ram and the selection of Rahim are independent events. The probability of both events happening together is the product of their individual probabilities.
Step 2: Detailed Explanation:
Let \( P(A) \) be the probability that Ram is selected: \( P(A) = \frac{7}{9} \).
Let \( P(B) \) be the probability that Rahim is selected: \( P(B) = \frac{4}{7} \).
The probability that both are selected is \( P(A \cap B) \).
For independent events:
\[ P(A \cap B) = P(A) \times P(B) \] Substituting the values:
\[ P(A \cap B) = \frac{7}{9} \times \frac{4}{7} \] Canceling the common factor \( 7 \) in the numerator and denominator:
\[ P(A \cap B) = \frac{4}{9} \] Step 3: Final Answer:
The probability that both are selected is \( \frac{4}{9} \).