Q.14. An experiment succeeds twice as often as it fails. Then the probability, that in the next 6 trails there will be atleast 4 successes , is
A. \frac{1}{729}
B. \frac{496}{729}
C. \frac{233}{729}
D. \frac{491}{729}
Answer:- B. \frac{496}{729}
Explanation :-
Experiment succeeds twice as often as it fails.
According to the given condition, if ‘p’ is success and ‘q’ is failure, then p=2q
p+q=1
2q+q=1
q=\frac{1}{3} and p=\frac{2}{3}
Here,n=6
Let X be the random variable
Therefore, X ∼ B(n,p)
Required probability = P(X ≥ 4 )
= P(X=4) + P(X=5) + P(X=6)
=6C4p4q2 + 6C5p5q + 6C6p6
= 15 x \left ( \frac{2}{3} \right )^{4}\left ( \frac{1}{3} \right )^{2}+6\left ( \frac{2}{3} \right )^{5}\left ( \frac{1}{3} \right )+\left ( \frac{2}{3} \right )^{6}
= \frac{496}{729}