Question

Sonal and Meenal appear in an interview for same post having two vacancies. If \(\frac 17\) is Sonal's probability of selection and \(\frac15\) is Meenal's probability of selection then what is the probability that only one of them is selected?

• A. \(\frac17\)
• B. \(\frac27\)
• C. \(\frac35\)
• D. \(\frac15\)

Answer 1

The Correct Option is B

Step 1: \(P(\text{both selected}) = \frac{1}{7}\times\frac{1}{5}=\frac{1}{35}\).
Step 2: \(P(\text{neither selected}) = \frac{6}{7}\times\frac{4}{5}=\frac{24}{35}\).
Step 3: \(P(\text{only one}) = 1-\frac{1}{35}-\frac{24}{35}=\frac{10}{35}\).
\[ \boxed{\frac{2}{7}} \]