TS EAMCET · Maths · Probability
If three numbers are randomly selected from the set \(\{1,2\), \(3, \ldots, 50\}\), then the probability that they are in arithmetic progression is
- A \(\frac{3}{50}\)
- B \(\frac{3}{98}\)
- C \(\frac{3}{49}\)
- D \(\frac{3}{25}\)
Answer & Solution
Correct Answer
(B) \(\frac{3}{98}\)
Step-by-step Solution
Detailed explanation
Total number of possible three numbers \(={ }^{50} \mathrm{C}_3\) \(=19,600\) \(a, b, c\) are in A.P. \(\Rightarrow 2 b=a+c=\) even Therefore a, c are either both even or both odd There are 25 odd and 25 even numbers in \(\{1, . .50\}\) Favourable case…
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