An experiment succeeds twice as often as it fails. The probability that in the next six trials there will be at least four successes, is:
It succeeds twice as often as it fails, so \(p = \frac{2}{3}\) and \(q = \frac{1}{3}\). With \(n = 6\):
\(P(X \ge 4) = \binom{6}{4}p^4q^2 + \binom{6}{5}p^5q + p^6\)
\(= \frac{15 \times 16 + 6 \times 32 + 64}{729} = \frac{240 + 192 + 64}{729} = \frac{496}{729}\)
Answer: (B) \(\frac{496}{729}\)
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