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An experiment succeeds twice as often as it fails. The probability of at least 5 successes in the six trials of this experiment is :

JEE · Math · previous-year question

  1. A.$${{240} \over {729}}$$
  2. B.$${{192} \over {729}}$$
  3. C.$${{256} \over {729}}$$correct
  4. D.$${{496} \over {729}}$$

Answer

C. $${{256} \over {729}}$$

Explanation

Probability of fail, P(F) = p $$ \therefore $$ Probability of success, P(S) = 2p We know, p + 2Pp = 1 $$ \Rightarrow $$ p = $${1 \over 3}$$ $$ \therefore $$ Now, probability of at least 5 success in 6 trials, P(x $$ \ge $$ 5) = P(x = 5) + P (x = 6) = 6C5 $${\left( {{2 \over 3}} \right)^5}{\left( {{1 \over 3}} \right)^1}{ + ^6}{C_6}{\left( {{2 \over 3}} \right)^6}{\left( {{1 \over 3}} \right)^o}$$ = $${\left( {{2 \over 3}} \right)^5}\left( {{6 \over 3} + {2 \over 3}} \right)$$ = $${{256} \over {729}}$$

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