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TS EAMCET · Maths · Probability

In an experiment a person gets success \(\alpha\) times out of \(\beta\) trails. If the experiment consists of \(n\) trials, then the probability that he fails at least \((n-1)\) times is

  1. A \(\frac{\alpha^{n-1}}{\beta^n}(n \beta-n \alpha+\alpha)\)
  2. B \(\frac{(\beta-\alpha)^{n-1}}{\beta^n}(n \alpha+\beta-\alpha)\)
  3. C \(\frac{\alpha^n}{\beta^n}(n \alpha+\beta)\)
  4. D \(\left(\frac{\beta-\alpha}{\beta}\right)^n(n \beta+n \alpha+1)\)
Verified Solution

Answer & Solution

Correct Answer

(B) \(\frac{(\beta-\alpha)^{n-1}}{\beta^n}(n \alpha+\beta-\alpha)\)

Step-by-step Solution

Detailed explanation

Probability for success \(p=\frac{\alpha}{\beta}\) Probability for failure \(q=\frac{\beta-\alpha}{\beta}\) Apply binomial theorem, Probability of atleast fails \((n-1)\) times means pass the exam at most one time. \(\mathrm{P}\) (fails atleast \((n-1)\) times)…