By applying binomial probability, the probability of getting at least four (4) successes is 0.9527.
In order to determine the probability of getting at least four (4) successes, we would apply binomial probability equation:
[tex]P =\; ^nC_r (p)^r (q)^{(n-r)}[/tex]
The probability of getting at least four (4) successes is given by:
P(x ≥ 4) = P(4) + P(5) + P(6)
Substituting the given parameters into the equation, we have;
P = ⁶C₄ × (0.85)⁴ × (0.15)³ + ₅C₆ × (0.85)⁵ × (0.15) + ⁶C₆ × (0.85) × (0.15)⁶
P = 0.17618 + 0.39933 + 0.37715
P = 0.9527.
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