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
- A \(\frac{\alpha^{n-1}}{\beta^n}(n \beta-n \alpha+\alpha)\)
- B \(\frac{(\beta-\alpha)^{n-1}}{\beta^n}(n \alpha+\beta-\alpha)\)
- C \(\frac{\alpha^n}{\beta^n}(n \alpha+\beta)\)
- D \(\left(\frac{\beta-\alpha}{\beta}\right)^n(n \beta+n \alpha+1)\)
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)…
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