Question

question 7
consider a binomial trial with n = 8 trials where the probability of success on a single trial is p = 0.30. enter your answers as
decimals rounded to 3 places.
a) what is the probability of getting exactly 3 successes?
enter answer
b) what is the probability of getting 3 or fewer successes?
enter answer
c) use the complement rule to find the probability of 4 or more successes.
enter answer
9 points

Explanation:

Step1: Calculate the probability of exactly 3 successes

The binomial probability formula is \(P(X = k)=C(n,k)\times p^{k}\times(1 - p)^{n - k}\), where \(n = 8\), \(k = 3\), \(p=0.3\), and \(C(n,k)=\frac{n!}{k!(n - k)!}\).

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Step2: Calculate the probability of 3 or fewer successes

\(P(X\leq3)=P(X = 0)+P(X = 1)+P(X = 2)+P(X = 3)\)

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Step3: Calculate the probability of 4 or more successes

Using the complement rule \(P(X\geq4)=1 - P(X\leq3)\)
\(P(X\geq4)=1 - 0.806 = 0.194\)

Answer:

a) \(0.254\)
b) \(0.806\)
c) \(0.194\)