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A bag contains 63 cards (numbered 1, 2, 3, 63). Two cards are picked at random from the bag (one after another and without replacement), what is the probability that the sum of numbers of both the cards drawn is even ?


A) \( \Large \frac{11}{21} \)

B) \( \Large \frac{34}{63} \)

C) \( \Large \frac{7}{11} \)

D) \( \Large \frac{11}{63} \)

E) Other than those given as options

Correct Answer:
E) Other than those given as options

Description for Correct answer:
even numbers from 1 to 63 = 31

Odd numbers from 1 to 63 = 32

When both cards are odd,

Probability = \( \Large \frac{32}{63} \) x \( \Large \frac{31}{62} \) = \( \Large \frac{16}{63} \)

When both cards are even,

Probability = \( \Large \frac{31}{63} \) x \( \Large \frac{30}{62} \) = \( \Large \frac{15}{63} \)

Required probability = \( \Large \frac{16}{63} \) + \( \Large \frac{15}{63} \) = \( \Large \frac{31}{63} \)

Part of solved SBI PO-Prelims2 questions and answers : Exams >> Bank Exams >> SBI PO-Prelims2




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