TS EAMCET · Maths · Probability
Out of the given 25 consecutive positive integers, three integers are drawn. If the least integer among given 25 integers is an odd number, then the probability that the sum of the three integers drawn is an even number is
- A \(\frac{289}{575}\)
- B \(\frac{286}{575}\)
- C \(\frac{288}{575}\)
- D \(\frac{287}{575}\)
Answer & Solution
Correct Answer
(A) \(\frac{289}{575}\)
Step-by-step Solution
Detailed explanation
Odd integers = 13, Even integers = 12. Total ways to choose 3 integers = \(\binom{25}{3} = \frac{25 \times 24 \times 23}{3 \times 2 \times 1} = 2300\). Favorable ways (sum is even) = \(\binom{\text{Even}}{3} + \binom{\text{Even}}{1}\binom{\text{Odd}}{2}\). =…
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