JEE Mains · Maths · STD 11 - 14. probability
Two integers are selected at random from the set \(\{1, 2, …, 11\}.\) Given that the sum of selected numbers is even, the conditional probability that both the numbers are even is
- A \(\frac {7}{10}\)
- B \(\frac {1}{2}\)
- C \(\frac {2}{5}\)
- D \(\frac {3}{5}\)
Answer & Solution
Correct Answer
(C) \(\frac {2}{5}\)
Step-by-step Solution
Detailed explanation
\(\mathrm{P}=\frac{\text { both number is even }}{\text { number of ways selecting two numbers such that their sum is even. }}\) \( = \frac{{{\,^5}{C_2}}}{{^5{C_2} + {\,^6}{C_2}}} = \frac{{10}}{{10 + 15}} = \frac{{10}}{{25}} = \frac{2}{5}\)
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