Respuesta :
A common discrete distribution is used in statistics, as opposed to a continuous distribution is called a Binomial distribution. The probability of getting at least 3 successes is 0.169.
What is Binomial distribution?
A common discrete distribution is used in statistics, as opposed to a continuous distribution is called a Binomial distribution. It is given by the formula,
P(x) = ⁿCₓ × (pˣ) × q⁽ⁿ⁻ˣ⁾
Where,
x is the number of successes needed,
n is the number of trials or sample size,
p is the probability of a single success, and
q is the probability of a single failure.
Given the probability of success is 0.25, while the probability of failure is 0.75. The probability of at least 3 success can be found by subtracting the probability of 0 success, 1 success, and 2 success from the entire probability, therefore, 1.
P(X≥3) = 1 - P(X=0) - P(X=1) - P(X=2)
= 1 - [⁶C₀ × (0.25)⁰ × (0.75)⁶] - [⁶C₁ × (0.25)¹ × (0.75)⁵] - [⁶C₂ × (0.25)² × (0.75)⁴]
= 1 - 0.356 - 0.297
= 0.169
Hence, the probability of getting at least 3 successes is 0.169.
Learn more about Binomial Distribution:
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