TS EAMCET · Maths · Probability
If \(\mathrm{X} \sim \mathrm{B}(7, \mathrm{p})\) is a binomial variate and \(\mathrm{P}(\mathrm{X}=3)=\mathrm{P}(\mathrm{X}=5)\) then \(\mathrm{p}=\)
- A \(\frac{5-\sqrt{10}}{3}\)
- B \(\frac{\sqrt{10}-2}{3}\)
- C \(\frac{5-\sqrt{15}}{2}\)
- D \(\frac{\sqrt{15}-3}{2}\)
Answer & Solution
Correct Answer
(C) \(\frac{5-\sqrt{15}}{2}\)
Step-by-step Solution
Detailed explanation
\(\binom{7}{3} \mathrm{p}^3 (1-\mathrm{p})^4 = \binom{7}{5} \mathrm{p}^5 (1-\mathrm{p})^2\) \(35 \mathrm{p}^3 (1-\mathrm{p})^4 = 21 \mathrm{p}^5 (1-\mathrm{p})^2\) \(35 (1-\mathrm{p})^2 = 21 \mathrm{p}^2\) \(5 (1-2\mathrm{p}+\mathrm{p}^2) = 3 \mathrm{p}^2\)…
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