JEE Mains · Maths · STD 12 - 13. probability
An experiment succeeds twice as often as it fails. The probability of at least \(5\) successes in the six trials of this experiment is
- A \(\frac{{496}}{{729}}\)
- B \(\frac{{192}}{{729}}\)
- C \(\frac{{240}}{{729}}\)
- D \(\frac{{256}}{{729}}\)
Answer & Solution
Correct Answer
(D) \(\frac{{256}}{{729}}\)
Step-by-step Solution
Detailed explanation
\(\text { Let } p(F)=p \Rightarrow p(S)=2 p\) \(p+2 p=1 \Rightarrow p=\frac{1}{3}\) \(p(x \geq 5)=p(x=5)+p(x=6)\) \( = {\,^6}{C_5}{\left( {\frac{2}{3}} \right)^5}{\left( {\frac{1}{3}} \right)^1} + {\,^6}{C_5}{\left( {\frac{2}{3}} \right)^6}{\left( {\frac{1}{3}} \right)^0}\)…
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